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The Relative Fit measure for evaluating a blockmodel

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Journal Paper Statistical Methods & Applications, Online First

Abstract

A blockmodel is a network in which the nodes are clusters of equivalent (in terms of the structure of the links connecting) nodes in the network being studied. The term block refers to the links between two clusters. When structural equivalence is relied on, two types of blocks are possible: complete blocks and null blocks. Ideally, all possible links are found in complete blocks while there are no links in null blocks. Yet, in the case of empirical networks, some links frequently appear in null blocks and some non-links appear in complete blocks. These links and non-links are called inconsistencies. When a relocation algorithm is applied to obtain a blockmodel, the criterion function is minimised. The number of inconsistencies is reflected in a criterion function’s value, leading to it being regularly used to fit an empirical network to an ideal blockmodel. Since the value of a criterion function depends on various factors (e.g. the block types allowed, the network size and its density), the values obtained for different networks are incomparable. To address this deficiency, the Relative Fit measure is proposed in this paper. Relative Fit values may be used to select the appropriate blockmodel type and/or number of clusters. Values of the Relative Fit measure can also be of value when fitting different empirical networks to a given blockmodel.

Identifikacija z rakom povezanih sporočil v spletni zdravstveni skupnosti MedOverNet

Marjan Cugmas, Gregor Petrič
Research Report Publisher: Faculty of Social Sciences, University of Ljubljana. City: Ljubljana. Year: 2020.

Abstract

Not avaiable.

Socialna opora starejših, ki živijo v domačem okolju, v času prvega vala epidemije koronavirusa v Sloveniji

Marjan Cugmas, Polona Dremelj, Tina Kogovšek, Anuška Ferligoj and Zenel Batagelj
Journal Paper Ars & Humanitas, Volume 15, Issue 1, Year 2021, Pages 73-90

Abstract

As a rapidly ageing country, Slovenia requires several societal adjustments. One is caring for older adults, who need various services and assistance due to age-related issues. These needs can be met via formal services (e.g., home care) or informal social support (e.g., relatives, friends, neighbours). Studies suggest that while some older adults have sufficient informal social sup-port, a significant number have little or none, making them particularly vulnerable in circum-stances such as the SARS-CoV-2 pandemic. This paper addresses the characteristics of informal social support for the elderly living at home during the first wave of the lockdown in Slovenia. The survey data comprise a probability sample of 605 older adults (65+) retrieved from the Jaz-Vem web panel. The survey measured various social support characteristics, such as the types of relationship with social support providers and geographical distance from them, as well as elements of formal social support. The results indicate that more than 10% of the sample had limited sources of social support, listing no providers or only geographically distant ones. In ad-dition, the amount and accessibility of social support providers during the pandemic was found to be related to the gender and household size of the older adults.

Global structures and local network mechanisms of knowledge-flow networks

Marjan Cugmas, Anuška Ferligoj, Miha Škerlavaj and Aleš Žiberna
Journal Paper PLOS ONE, Volume 16, Issue 2, Year 2021, Pages e0246660

Abstract

Understanding the patterns and underlying mechanisms that come into play when employees exchange their knowledge is crucial for their work performance and professional development. Although much is known about the relationship between certain global network properties of knowledge-flow networks and work performance, less is known about the emergence of specific global network structures of knowledge flow. The paper therefore aims to identify a global network structure in blockmodel terms within an empirical knowledge-flow network and discuss whether the selected local network mechanisms are able to drive the network towards the chosen global network structure. Existing studies of knowledge-flow networks are relied on to determine the local network mechanisms. Agent-based modelling shows the selected local network mechanisms are able to drive the network towards the assumed hierarchical global structure.

blockmodeling: an R package for Generalized Blockmodeling

Miha Matjašič, Marjan Cugmas and Aleš Žiberna
Journal Paper Metodološki zvezki, Volume 17, Issue 2, Year 2020, Pages 49-66

Abstract

This paper presents the R package blockmodeling which is primarily meant as an implementation of generalized blockmodeling (more broadly blockmodeling) for valued networks where the values of the ties are assumed to be measured on at least interval scale. Blockmodeling is one of the most commonly used approaches in the analysis of (social) networks, which deals with the analysis of relationships or connections, between the units studied (e.g., peoples, organizations, journals etc.). The R package blockmodeling implements several approaches for the generalized blockmodeling of binary and valued networks. Generalized blockmodeling is commonly used to cluster nodes in a network with regard to the structure of their links. The theoretical foundations of generalized blockmodeling for binary and valued networks are summarized in the paper while the use of the R package blockmodeling is illustrated by applying it to an empirical dataset.

Blockmodeling dynamic networks: a Monte Carlo simulation study

Marjan Cugmas and Aleš Žiberna
Conference Paper Conference: Applied Statistics 2021. City: Online. Year: 2021.

Abstract

Social network analysis methodology is essential for studying the relationships among units when networks operationalise such relationships. For example, suppose the aim is to identify groups of equivalent units (according to their links) and the links among the groups so obtained, for which a researcher can apply blockmodeling. Moreover, suppose that several networks are observed regarding the same units at different points in time. In this case, specific blockmodeling approaches are available for use. An overview of some of these blockmodeling approaches is to be provided in this presentation, while differences among them are to be highlighted. Alongside this general overview, a Monte Carlo simulation study is described that empirically evaluates the differences among these blockmodeling approaches. Various factors are considered in this study, such as blockmodel type, blocks’ densities, the stability of groups in time, local network mechanisms, and network size. The study results indicate that while separate analyses of networks at different time points prove sufficient in some in particular other cases. General guidelines on the use of one approach or another will be given.

Comparing different approaches to blockmodeling dynamic networks

Marjan Cugmas and Aleš Žiberna
Conference Paper Conference: EUSN 2021. City: Online. Year: 2021.

Abstract

Blockmodeling aims to reduce large and complex networks to smaller, comprehensive, and more interpretable structures (Doreian et al. 2005). Several blockmodeling approaches to blockmodeling dynamic (i.e., measured at several time points) networks (e.g., Matias and Miele 2017, Bartolucci and Pandolfi 2020, Bar-Hen et al. 2020, Žiberna 2020) have been proposed in recent years. These approaches have yet to be thoroughly compared on empirical network data. Therefore, the preliminary results of a Monte Carlo study that addressed this issue will be presented. Special attention is paid to the algorithms for generating dynamic networks with a specified blockmodel and partition. These algorithms generate links by considering different local network mechanisms like mutuality, popularity, and transitivity. These generated networks are argued to more closely represent real-world networks. The networks are generated so that the blockmodel type and partition can change in time.

The social support of older adults during the first wave of coronavirus epidemic in Slovenia

Marjan Cugmas, Anuška Ferligoj, Tina Kogovšek and Zenel Batagelj
Conference Paper Conference: EUSN 2021. City: Online. Year: 2021.

Abstract

Measures for preventing the spread of SARS-CoV-2 coronavirus in the first wave of the epidemic have significantly impacted the availability of aid sources. The lockdown might affect the elderly population even more since many are heavily dependent on the help of others and, at the same time, more vulnerable in the event of coronavirus infection. Specific forms of formal assistance at home are available to the elderly, but informal sources of help (social support) are essential. Furthermore, adequate social support is crucial in maintaining physical and mental health. Hence, the present study addresses the emergence of different social support network types among the elderly living at home during the first wave of the coronavirus epidemic. As part of the survey, a representative and probabilistic sample of people over 64 years old was collected between 25 April and 4 May 2020. In the online survey, respondents listed and described the persons they turn to for various kinds of help (socializing, emotional support, instrumental support). The ego-centred networks were formed based on these data and analyzed by clustering of symbolic data. The obtained clusters are mostly consistent with those obtained within the earlier studies. Regarding the accessibility of social support, the results show that more than half of the elderly have sufficient social support networks, but the share of people without any social support is high.

Choosing the number of clusters and blockmodel type based on the Relative Fit measure

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: Networks 2021. City: Online. Year: 2021.

Abstract

A blockmodel is a network where the nodes are clusters of equivalent (according to the structure of the links) units from the studied network. The term block refers to a submatrix showing the links between two clusters. When the structural equivalency is used, the two types of blocks are possible: complete blocks and null blocks. Ideally, there are all possible links in complete blocks while there is no link in the null block. However, some links frequently appear in null blocks in empirical networks, and some non-links appear in complete blocks. Such links and non-links are called inconsistencies. The number of inconsistencies is reflected by a criterion function when the relocation algorithm for generalized blockmodeling is used. Therefore, a criterion function can be used as a fit function of an empirical network to a chosen blockmodel. Because the value of a criterion function depends on many factors (e.g., network size, density), the Relative Fit measure was proposed. Its expected value in the case of random networks is 0, and the maximum value is 1 (the case without inconsistencies). It is argued that the values of the Relative Fit measure, obtained on different empirical networks, are comparable. Therefore, the presentation addresses whether the Relative Fit measure can be efficiently used for choosing an appropriate blockmodel type and the number of clusters. The research question is addressed by Monte Carlo simulations in which different blockmodel types, number of clusters and amounts of inconsistencies are considered. The results show that the Relative Fit measure can be used to select the appropriate number of clusters and/or blockmodel type when the amount of inconsistencies is not too high.

Scientific collaboration of researchers and organizations: A two-level blockmodeling approach

Marjan Cugmas, Franc Mali and Aleš Žiberna
Conference Paper Conference: Complex Networks 2020. City: Online. Year: 2020.

Abstract

Understanding scientific collaboration (SC) patterns among researchers on different social levels is fundamental for the development and successful implementation of the R&D policies. Therefore, the study aims to provide a simultaneous insight into the SC patterns among individual researchers (individual level) and institutions (institutional level). Considering different social levels is important because SC on different levels are interdependent. In this study, SC on an individual level is operationalized by co-authorship of scientific paper while two institutions are said to collaborate if they collaborated on a joint research project. The data were retrieved by the Slovene information systems that contain information about researches and organizations that are registered at the Slovene research agency. Based on these data, the two-level SC networks were constructed for the researchers from the field of Social sciences and their institutions. The data for the period between 2005 and 2015 are analyzed by using the k-means-based blockmodeling approach for linked networks that enable to simultaneously blockmodel different levels of multi-level networks. The results for different levels are interpreted. The analysis of the two-mode network reveals that their institution membership in a large part determines the SC on an individual level.

Types of social support networks of elderly people during SARS-Cov-2 coronavirus pandemic

Marjan Cugmas, Anuška Ferligoj and Tina Kogovšek
Conference Paper Conference: SUNBELT COVID 2020. City: Online. Year: 2020.

Abstract

The aging of population requires adjustments from the society in providing additional types of services and assistance to the elderly population. These can be provided by formal services and informal social support. The latter are especially important, as it has been shown that the lack of social support is related to a lower level of psychological as well as physical well-being. Therefore, the current study aims to identify and describe types of the ego-centered social support networks of elderly people during the SARS-Cov-2 coronavirus pandemic. To this aim, the survey among Slovenians, older than 64 years was conducted (from April 25 till May 4, 2020) on the probability Web-panel based sample (n = 605). The ego-networks were clustered by hierarchical clustering approach for symbolic data. The clustering was done for different types of social support (socializing, instrumental support and emotional support) and variables describing the characteristics of the supporting network (i.e., type of relationship, number of contacts, geographical distance). The results are especially important for sustainable care policy planning as well as for crisis interventions planning.

A two-level blockmodeling of scientific collaborations of Slovenian researchers and institutions

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: SUNBELT 2020. City: Online. Year: 2020.

Abstract

Understanding scientific collaboration (SC) patterns among researchers on different social levels is fundamental for the development and successful implementation of the R&D policies. Therefore, the aim of the presented study is to provide a simultaneous insight into the SC patterns among individual researchers (individual level) and among institutions (institutional level). Considering different social levels is especially important because collaborations on different levels are interdependent. In this study, SC on an individual level is operationalized by co-authorship of scientific paper while two institutions are said to collaborate if they jointly applied for a research project. The data for the analysis were retrieved by Slovene information systems that contains information (including personal bibliographies) about all researches and organizations that are registered at the Slovene research agency (ARRS). Based on these data, the two-level collaboration networks were formed for the researchers that are classified under the field of Social sciences according to the ARRS classification scheme and their institutions. The data for the period between 1995 and 2015 are analysed by using k-means-based blockmodeling approach for linked networks (Žiberna, 2019) that enable to simultaneously blockmodel different levels of multi-level networks. The results for the individual level, institutional level and two-mode network connecting them are interpreted. On the individual level, a typical multi-core—semi-periphery structure of SC appears. The researchers within the core groups are internally well linked while the ones from semi-periphery are generally less linked to each other. Some researchers from different core groups are more or less linked to each other. On the institutional level, a core-cohesive structure (Cugmas et al., 2020) can be recognized. This is a structure with (i) a group of internally and externally highly linked institutions (called core group), and (ii) several cohesive groups that are linked to the core group but not to the other cohesive groups. A group of organizations, that are generally not linked to other institutions, and several organizations that are clustered in their own clusters also appear. The analysis of the two-mode network reveals that the clustering of researchers in is in a large part determined by their institution membership.

Social support networks of elderly people during SARS-Cov-2 coronavirus pandemic

Anuška Ferligoj, Marjan Cugmas, Tina Kogovšek and Zenelj Batagelj
Conference Paper Conference: COSTNET COVID 2020. City: Online. Year: 2020.

Abstract

The aging of population requires adjustments from the society in providing additional types of services and assistance to the elderly population. These can be provided by formal services and informal social support. The latter are especially important, as it has been shown that the lack of social support is related to a lower level of psychological as well as physical well-being. During the SARS-Cov-2 coronavirus pandemic, the lack of social support for elderly people is even more crucial because of the social distancing. Therefore, the current study aims to identify and describe types of the ego-centered social support networks of elderly people during the coronavirus pandemic. To this aim, the survey among Slovenians, older than 64 years was conducted (from April 25 till May 4, 2020) on the probability Web-panel based sample (n = 605). The ego-networks were clustered by hierarchical clustering approach for symbolic data. The clustering was done for different types of social support (socializing, instrumental support and emotional support) and variables describing the characteristics of the supporting network (i.e., type of relationship, number of contacts, geographical distance). The results are especially important for sustainable care policy planning as well as for crisis interventions planning also for the next possible waves of coronavirus.

The emergence of the global network structure of knowledge-flow networks

Marjan Cugmas, Aleš Žiberna, Anuška Ferligoj and Miha Škerlavaj
Conference Paper Conference: COSTNET 2019. City: Bilbao, Spain. Year: 2019.

Abstract

Knowledge-flow networks describe how the knowledge is exchanged among the units. They are usually observed within different companies since understanding patterns and underlaying mechanisms of exchanging knowledge among the employees is crucial to ensure the competitiveness of a company. The presentation addresses the evolution of a global network structure of the knowledge-flow networks by considering the selected local network mechanisms.

The empirical data are analyzed by blockmodeling approach to identify the global network structure of the knowledge-flow networks. The data were collected among the employees in the international company. The results show that the global network structure is approaching to the hierarchical one in time.

Once the global network structure is identified, the algorithm from the family of the network evolution models is used to test if the selected local network mechanisms can drive the global network structure towards the hierarchical one. The algorithm and the selected mechanisms are based on the theory proposed by Nebus (2006). By following his theory, the employees are considering the costs and the benefits of asking for advice to a given unit. It is confirmed, by the Monte Carlo simulations, that the hierarchical global network structure can emerge as a consequence of the mechanisms which are related to the hierarchical position of the units, tenure of the units, popularity level of the units, homophily of the shared partners and distance between the ego and the alter.

The local network mechanisms and hierarchical global network structure in the context of knowledge-flow

Marjan Cugmas, Aleš Žiberna, Miha Škerlavaj and Anuška Ferligoj
Conference Paper Conference: Applied Statistics 2019. City: Ribno, Slovenia. Year: 2019.

Abstract

The research results, presented in this talk, were obtained within a larger study, of which the aim was to understand the relationship between the local network mechanisms and the global network structures. Due to the scope of this research question, the focus will be given on the local network mechanisms that can drive the global network structure towards hierarchical one. Since the local network mechanisms and the global network structures should be studied within a social context, the knowledge-flow networks were analyzed. The data were collected at three time points, between 2004 and 2007, among the employees in the middle size knowledge-based company in Slovenia. The results showed that the emerged global structure of knowledge-flow network resembles a hierarchical one. The local network mechanisms were chosen based on the previous studies on the emergence and dynamics of the knowledge-flow networks. Such mechanisms are popularity of a unit, hierarchical position of a unit, the network distance between two units, transitivity, tenure and others. By using the algorithm from the family of the network evolution models, it was shown that hierarchical global network structure can emerge as a consequence of the selected local network mechanisms. The results are especially important because the nodes’ attributes were not taken into account (except the tenure, which can be easily estimated from the network) when generating the networks. The practical implication of this is a cognition that a company can define some policies, which are independent on the characteristics of the employees, and which would drive the structure of the knowledge-flow towards the hierarchical one.

On the Local Network Mechanisms and the Global Network Structures

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: EUSN 2019. City: Zurich, Switzerland. Year: 2019.

Abstract

Understanding the link between micro social mechanisms and macro social output is one of the central interests of social scientists. In the context of social networks, different micro social mechanisms are operationalized by local network mechanisms while macro social outputs by global network structures. The relationship between the selected local network mechanisms and the selected global network structures is addressed in this presentation.

A global network structure is operationalized by a blockmodel which is a network where the nodes are clusters of equivalent units from the studied network (Doreian, Batagelj, and Ferligoj, 2005). As the selection of the local network mechanisms and the global network structure depend on the social context of the study, two such contexts will be considered in the second part of the presentation. Firstly, based on the observations of the interactional networks of preschoolers, the symmetric core-cohesive blockmodel type will be defined. It is a combination of the well-known symmetric core-periphery blockmodel and cohesive blockmodel. It will be shown that the most commonly treated local network mechanisms (mutuality, popularity, assortativity and different types of transitivity-related mechanisms) can cause the emergence of this blockmodel. Secondly, the hierarchical blockmodel that appears in many companies when measuring knowledge-flow will be considered. For the growing networks with the hierarchical blockmodel, it will be shown that the tenure or the hierarchical position of the units have an important impact on the group formation. Yet, the hierarchical structure can emerge also when tenure is not included as a mechanism, but the following many times mentioned mechanisms in this context are considered: popularity, hierarchy, transitivity and distance between two units.

The emergence of the global network structure in kindergarten: a simulation approach

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: YSM 2018. City: Balatonfüred, Hungary. Year: 2018.

Abstract

The analysis of the interactional networks, collected among pre-school children (Head Start preschools, United States, data collected in 2004—2006) will be presented in order to show that the proposed symmetric core-cohesive blockmodel type can appear in such empirical networks.

A blockmodel is a network where the units are clusters of units from the studied network. The term block refers to a submatrix showing the links between two clusters. The symmetric core-cohesive blockmodel consists of three or more clusters. The units from each cluster are internally well linked while those from different clusters are ideally not linked to each other. The exception are the units from so called "core cluster". These units have a mutual links to all the units in the network. The other clusters are called "cohesive clusters".

After the analysis of the empirical networks, the presentation will address the main research question, which is whether the proposed blockmodel type can emerge as a consequence of the selected social mechanisms. The characteristics of the units are not considered. The social network mechanisms that will be considered, i.e., popularity, transitivity, mutuality and assortativity, have been extensively studied in not only interactional networks among pre-school, but also in many other types of networks. The Monte Carlo simulations are used to answer the main research question.

Local mechanisms of knowledge-flow in growing networks

Marjan Cugmas, Anuška Ferligoj, Miha Škerlavaj, Nada Zupan and Aleš Žiberna
Conference Paper Conference: XX April International Academic Conference On Economic and Social Development. City: Moscow, Russia. Year: 2019.

Abstract

Understanding patterns and underlaying mechanisms of exchanging knowledge among the employees is crucial to ensure the competitiveness of a company. Moreover, various patterns of knowledge transfer are closely related to employee performance and development. In a current study, the exchanging knowledge among the employees is called knowledge-flow. Knowledge-flow can be studied by using the social network analysis methodology. In the data collection procedure, the employees were asked to list those by whom they received different kinds of knowledge. Directed networks can be constructed based on such data. Here, nodes are employees and arrows are operationalizations of knowledge-flow.

Knowledge-flow on the level of a company can be analyzed by using blockmodeling. Blockmodeling is an approach to reduce a large, potentially incoherent networks, to a smaller and more interpretable networks. In such network, nodes represent clusters of equivalent employees.

Blockmodeling is applied on the knowledge-flow networks, collected in the middle size knowledge-based company in Slovenia (the data were collected in three time points, between 2004 and 2007). The aim is to understand the underlying mechanisms of the knowledge-flow in the company. Different mechanisms are considered: hierarchy, distance, tenure, homophily of gender, tenure and business unit and others. Based on the observations in the empirical networks, the Monte Carlo simulations are used to generate the networks by considering some selected local network mechanisms. The global network structures of the generated networks are then compared to the empirical ones.

The social support networks of elderly people in Slovenia during the Covid-19 pandemic

Marjan Cugmas, Anuška Ferligoj, Tina Kogovšek, Zenel Batagelj
Journal Paper PLOS ONE, Volume 16, Issue 3, Year 2021, Pages e0247993

Abstract

Population ageing requires society to adjust by ensuring additional types of services and assistance for elderly people. These may be provided by either organized services and sources of informal social support. The latter is especially important since a lack of social support is associated with a lower level of psychological and physical well-being. During the Covid-19 pandemic, social support for the elderly has proven to be even more crucial, also due to physical distancing. Therefore, this study aims to identify and describe the various types of personal social support networks of the elderly population during the coronavirus pandemic. To this end, a survey of Slovenians older than 64 years was conducted from April 25 to May 4, 2020 on a probability Web-panel-based sample (n = 605). The ego-networks were clustered by a hierarchical clustering approach for symbolic data. Clustering was performed for different types of social support (socializing, instrumental support, emotional support) and different characteristics of the social support networks (i.e., type of relationship, number of contacts, geographical distance). The results show that most of the elderly population in Slovenia have a satisfactory social support network, while the share of those without any (accessible) source of social support is significant. The results are particularly valuable for sustainable care policy planning, crisis intervention planning as well as any future waves of the coronavirus.

Scientific collaboration of researchers and organizations: A two-level blockmodeling approach

Marjan Cugmas, Franc Mali, Aleš Žiberna
Journal Paper Scientometrics, Volume 125, Issue 3, Year 2020, Pages 2471–2489

Abstract

The development and successful implementation of R&D policies depends on understanding patterns of scientific collaboration (SC). Existing studies on SC typically focus on the individual level, despite SC occurring on many interdependent social levels. Therefore, this paper provides a simultaneous insight into SC patterns among researchers (individual level) and among organizations (organizational level) in the social sciences. SC on the individual level is operationalized by co-authorship of a scientific paper whereas two organizations are said to collaborate if they share a research project. Based on data for the period 2006–2015 retrieved from Slovenian national information systems, two-level collaboration networks were formed with respect to researchers in the social sciences field. These networks were analyzed using a k-means-based blockmodeling approach for linked networks. The results show a high level of interdisciplinary SC and a large organizational impact on individual collaborations. On the individual level, a structure with several cohesive clusters and a semi-periphery appears while, on the organizational level, a kind a core–periphery structure emerges in which both the core and periphery can be split into several clusters. The most surprising result indicates that SC on the level of organizations is often not reflected in common published scientific papers on the individual level (and vice versa).

Symmetric core-cohesive blockmodel in preschool children's interaction networks

Marjan Cugmas, Dawn DeLay, Aleš Žiberna and Anuška Ferligoj
Journal Paper PLOS ONE, Volume 15, Issue 1, Year 2020, Pages e0226801

Abstract

Researchers have extensively studied the social mechanisms that drive the formation of networks observed among preschool children. However, less attention has been given to global network structures in terms of blockmodels. A blockmodel is a network where the nodes are groups of equivalent units (according to links to others) from a studied network. It is already shown that mutuality, popularity, assortativity, and different types of transitivity mechanisms can lead the global network structure to the proposed asymmetric core-cohesive blockmodel. Yet, they did not provide any evidence that such a global network structure actually appears in any empirical data. In this paper, the symmetric version of the core-cohesive blockmodel type is proposed. This blockmodel type consists of three or more groups of units. The units from each group are internally well linked to each other while those from different groups are not linked to each other. This is true for all groups, except one in which the units have mutual links to all other units in the network. In this study, it is shown that the proposed blockmodel type appears in empirical interactional networks collected among preschool children. Monte Carlo simulations confirm that the most often studied social network mechanisms can lead the global network structure to the proposed symmetric blockmodel type. The units’ attributes are not considered in this study.

Mechanisms generating asymmetric core-cohesive blockmodels

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Journal Paper Advances in methodology and statistics, Volume 1, Issue 1, Year 2019, Pages 17–41

Abstract

The paper addresses the relationship between different local network mechanisms and different global network structures, described by blockmodels. The research question is narrowed to the context of preschool children networks. Based on the studies regarding friendship, liking and interactional networks among preschool children, the popularity, transitivity, mutuality and assortativity mechanisms are assumed to be important for the evolution of such networks. It is assumed that the global network structure is defined by an asymmetric core-cohesive blockmodel consisting of one core group of units and two or more cohesive groups of units. Therefore, the main research question is whether the emergence of an asymmetric core-cohesive blockmodel can be a result of the influence of the listed mechanisms. Different initial global network structures are considered. Monte Carlo simulations were used. The relative fit measure is proposed and used to compare different blockmodel types on generated networks. The results show that the listed mechanisms indeed lead to the assumed global network structure.

The personal factors in scientific collaboration: views held by Slovenian researchers

Franc Mali, Toni Pustovrh, Marjan Cugmas and Anuška Ferligoj
Journal Paper Corvinus Journal of Sociology and Social Policy, Volume 9, Issue 2, Year 2018, Pages 3–24

Abstract

Scientific collaboration (SC) has become a widespread feature of modern research work. While many social network studies address various aspects of SC, little attention has so far been given to the specific factors that motivate researchers to engage in SC at the individual level. In our article, we focus on the types and practices of SC that researchers in Slovenia engage in. We consider this topic by adopting a quantitative and qualitative methodological approach. The former was conducted through a web survey among active researchers, and the latter through in-depth interviews with a selected group of top researchers, i.e. intellectual leaders. Results show the extent of individual SC depends on the perceptions of researchers of the benefits of SC. Qualitative interviews additionally provide broader reflections on certain policy mechanisms that could better motivate Slovenian scientists to scientifically collaborate in the international arena.

Comparing Two Partitions of Non-Equal Sets of Units

Marjan Cugmas and Anuška Ferligoj
Journal Paper Advances in Methodology and Statistics, Volume 15, Issue 1, Year 2018, Pages 1–21

Abstract

Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions. Sometimes, e.g. when the units are observed in two time periods, the splitting and merging of clusters should be considered differently, according to the operationalization of the stability of clusters. The Rand Index is symmetric in the sense that both the splitting and merging of clusters lower the value of the index. In such a non-symmetric case, one of the Wallace indexes (Wallace, 1983) can be used. Further, there are several cases when one wants to compare two partitions obtained on different sets of units, where the intersection of these sets of units is a non-empty set of units. In this instance, the new units and units which leave the clusters from the first partition can be considered as a factor lowering the value of the index. Therefore, a modified Rand index is presented. Because the splitting and merging of clusters have to be considered differently in some situations, an asymmetric modified Wallace Index is also proposed. For all presented indices, the correction for chance is described, which allows different values of a selected index to be compared.

Generating global network structures by triad types

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Journal Paper Plos ONE, Volume 13, Issue 5, Year 2018, Pages e0197514

Abstract

This paper addresses the question of whether one can generate networks with a given global structure (defined by selected blockmodels, i.e., cohesive, core-periphery, hierarchical, and transitivity), considering only different types of triads. Two methods are used to generate networks: (i) the newly proposed method of relocating links; and (ii) the Monte Carlo Multi Chain algorithm implemented in the ergm package in R. Most of the selected blockmodel types can be generated by considering all types of triads. The selection of only a subset of triads can improve the generated networks’ blockmodel structure. Yet, in the case of a hierarchical blockmodel without complete blocks on the diagonal, additional local structures are needed to achieve the desired global structure of generated networks. This shows that blockmodels can emerge based only on local processes that do not take attributes into account.

The stability of co-authorship structures

Marjan Cugmas, Anuška Ferligoj and Luka Kronegger
Journal Paper Scientometrics, Volume 106, Issue 1, Year 2015, Pages 163-186

Abstract

This article examines the structure of co-authorship networks’ stability in time. The goal of the article is to analyse differences in the stability and size of groups of researchers that co-author with each other (core research groups) formed in disciplines from the natural and technical sciences on one hand and the social sciences and humanities on the other. The cores were obtained by a pre-specified blockmodeling procedure assuming a multi-core–semi-periphery–periphery structure. The stability of the obtained cores was measured with the Modified Adjusted Rand Index. The assumed structure was confirmed in all analysed disciplines. The average size of the cores obtained is higher in the second time period and the average core size is greater in the natural and technical sciences than in the social sciences and humanities. There are no differences in average core stability between the natural and technical sciences and the social sciences and humanities. However, if the stability of cores is defined by the splitting of cores and not also by the percentage of researchers who left the cores, the average stability of the cores is higher in disciplines from the scientific fields of Engineering sciences and technologies and Medical sciences than in disciplines of the Humanities, if controlling for the networks’ and disciplines’ characteristics. The analysis was performed on disciplinary co-authorship networks of Slovenian researchers in two time periods (1991–2000 and 2001–2010).

Anonymous: the problems, dilemmas and desires of Slovenian adolescents in online counselling

Ksenija Lekić, Nuša Konec Juričič, Petra Tratnjek, Marjan Cugmas, Darja Kukovič and Borut Jereb
Journal Paper Slovenian Nursing Review, Volume 48, Issue 2, Year 2014, Pages 78-87

Abstract

Introduction: Online counselling represents a new medium for finding health information. The aim of the research is to determine the importance of analysis of adolescents' issues in order to understand their problems, needs and desires. Methods: In 2012 the system for the classification of questions by the type of problem was introduced. In relation to the contents the questions were first sorted to the parent category then followed by the categorization according to the subject matter. The calculation comprised the portions, averages and quartiles, and in some cases even Cramer's V coefficients. The analysis covered the entire defined population (3,257 coded questions). Results: Most of the users are girls (76 %), the most representative group encompasses adolescents aged between 14 and 17 years (57 %). Most questions were grouped into the categories Sexuality and sexual health (24 %), Relationships (23 %) and Body (20 %). The length of posts increases with the age of the user (Cr's V = 0.18), but differs by the gender (a higher proportion of longer questions (Cr's V = 0.15) were posted by girls) and the themes (Cr's V = 0.31). Discussion and conclusion: The categorizing of questions is suitable for the identification and analysis of adolescents' problems, needs and desires. Regular categorisation of questions with analysis will serve as a useful research tool for youth work.

Finding target segments for raising awareness about depression using decision trees

Marjan Cugmas and Aleš Žiberna
Journal Paper Teorija in praksa, Volume 54, Issue 5, Year 2015, Pages 886–906

Abstract

The purpose of this paper is to determine whether decision trees can be used to distinguish between those who are more and those who are less prone to depression and mental ill-being based on demographic and some other identifiable characteristics of individuals. Using decision trees we wanted to find segments which could be targeted in awarenessraising programs about depression. By analysing data from the European Social Survey in 2012 for Slovenia, we identified four groups at a greater risk of depression: young unemployed, unemployed passive, older people and women older than 52 years. Decision trees are also shown for finding target segments in the field of mental well-being. The results confirm the findings of previous studies.

Scientific co-authorship networks

Marjan Cugmas, Anuška Ferligoj, Luka Kronegger
Book Editors: Patrick Doreian, Vlado Batagelj and Anuška Ferligoj. Publisher: Wiley. Year: 2020.

The paper addresses the stability of the co-authorship networks in time. The analysis is done on the networks of Slovenian researchers in two time periods (1991-2000 and 2001-2010). Two researchers are linked if they published at least one scientific bibliographic unit in a given time period. As proposed by Kronegger et al. (2011), the global network structures are examined by generalized blockmodeling with the assumed multi-core--semi-periphery--periphery blockmodel type. The term core denotes a group of researchers who published together in a systematic way with each other. The obtained blockmodels are comprehensively analyzed by visualizations and through considering several statistics regarding the global network structure. To measure the stability of the obtained blockmodels, different adjusted modified Rand and Wallace indices are applied. Those enable to distinguish between the splitting and merging of cores when operationalizing the stability of cores. Also, the adjusted modified indices can be used when new researchers occur in the second time period (newcomers) and when some researchers are no longer present in the second time period (departures). The research disciplines are described and clustered according to the values of these indices. Considering the obtained clusters, the sources of instability of the research disciplines are studied (e.g., merging or splitting of cores, newcomers or departures). Furthermore, the differences in the stability of the obtained cores on the level of scientific disciplines are studied by linear regression analysis where some personal characteristics of the researchers (e.g., age, gender), are also considered.

Srečanja na spletu: potrebe slovenske mladine in spletno svetovanje

Ksenija Lekić, Petra Tratnjek, Nuša Konec Juričič and Marjan Cugmas
Book Editors: Alenka Tacol, Žarka Brišar-Slana, Brane But, Ksenija Centa, Lucija Gobov, Metka Kuhar. Publisher: National Institute of Public Health. City: Ljubljana. Year: 2014.

Knjiga Srečanja na spletu odstira več kot desetletje dolgo in bogato prakso spletnega svetovanja mladostnikom v svetovalni mreži To sem jaz, kjer ima mladostnik enostaven, anonimen, brezplačen in hiter dostop do strokovnega nasveta.

Sex education in the context of health education in Slovenian secondary school

Aleksandra Žalar, Evita Leskovšek, Fani Čeh, Marjan Cugmas
Book Publisher: Institute of Public Health of the Republic of Slovenia. City: Ljubljana. Year: 2013.

Abstract

The survey done in spring 2012, in which participated 890 randomy selected students, from Slovenian hight schools, brings us to an answers on the questions related with contentment of sexual education and opinions about introduce it (for those who has not yet linstening it in the schools). In addition, they also examine the knowledge in the relation with contraception and sexual transmitted diseases. Furthermore, it involves answeres on perceptions of sexual harassment and potentional experience with it.
The results are comparable with previous researches and indicate the need for the introduction of contents related with sexuality in the educational process. As well, it warns on the low level of knowledge of sexual diseases and hightlights the meaning and role of the public media, especially the Internet, in the forwarding the content related to sexuality.

Classification of Scientific Disciplines According to Types of Scientific Publications

Marjan Cugmas
Bachelor's Thesis Menthors: Franc Mali and Luka Kronegger. Institution: Faculty of Social Sciences, University of Ljubljana. Year: 2013.

Abstract

Countries, companies and other interest groups are increasingly investing into science and scientific research. As a result, assessment in science is becoming more important, while the search of optimal indicators of scientific output often raises the question of how the indicators reflect the complex structure of scientific activity.
The thesis is founded on the findings of Slovenian and foreign authors discussing the variety of scientific activity in individual scientific disciplines. It first presents the disciplines and proceeds by studying the optimality of assessing scientific output, as defined by the Slovenian Research Agency (ARRS), based on information for the period 1985-2010 obtained using the databases SICRIS and COBISS. Scientific output is assessed through bibliographic units in individual disciplines. The findings of Ward’s method of hierarchical cluster analysis indicate that the classification proposed by the ARRS fails to reflect the specifics of bibliographic habits in given disciplines within different sciences. In addition to the specifically defined goal, the analysis reveals important information about the dynamics of the publication of various groups of Slovenian scientists.

Stability of co-authorship blockmodels

Marjan Cugmas
Master's Thesis Menthor: Anuška Ferligoj. Institution: University of Ljubljana, Faculty of electrical engineering. Year: 2015.

Abstract

Collaboration in science plays an important role in the production as in the dissemination of a new scientific knowledge. Even there is hard to determine the borders of scientific collaboration, the term is often operationalized through the co-authorship of scientific bibliographic units, which represents one of the most important results of a scientific collaboration. Based on the personal researchers' bibliographies, the co-authorship networks can be constructed. These networks enable us to study the relationship between some researchers' characteristics and the patterns of establishing new co-authorship ties. Furthermore, it allows us to study the structure of that kind of networks.
Kronegger et al. (2011), who studied the co-authorship networks of four scientific disciplines in four five years periods, confirmed the hypothesis about the multi-core-semi-periphery|periphery structure. In the current work, the analysis is done on the level of almost all scientific disciplines, according to the Slovenian Research Agency (ARRS). Beside the structure of co-authorship networks, the current work also addresses the question of the stability of scientific collaboration teams across scientific fields.
The structure of co-authorship networks of Slovenian researchers is examined using the pre-specified blockmodeling, while the stability of obtained clusters of researchers is measured with one of three proposed Modified Adjusted Rand Indices. In the context of co-authorship networks in two time periods, some researchers can enter or leave the network in the second time period. This implies that the classification (blockmodeling) is performed on two different sets of units for the first and for the second time period. The Modified Adjusted Rand Indices enable us to compare two clusterings, obtained on two different sets of units, where one set of units is a subset of another set of units. Moreover, the merging and splitting of clusters in time have a different effects on the value of proposed indices.
The assumed network structure multi-core-semi-periphery|periphery exists in all analysed scientific disciplines. The average core size is statistically significantlly (p < 0.05) higher in the first time period (5.6 researchers) compared to the second time period (4.4 researchers). Depending on the field, the average core size is statistically significant (p < 0.05) higher in the fields of the natural and technical sciences (4.6 researchers) that in the fields of the Social sciences and Humanities (3.8 researchers). The stability of cores on the level of scientific disciplines is relatively low. Instability of cores is more the consequence of many short term collaborations rather than splitting of cores. On the level of scientific fields, the average stability of cores is statistically significant (p < 0.05) higher in the fields of the Engineering sciences and technologies and the Medical sciences in comparison to the Humanities, while on the level of merged scientific fields into the natural and technical sciences and social sciences and humanities, there is no difference in the average stability of obtained cores (the value of MARI1 is 0.21).

Local mechanisms affecting the evolution of blockmodels

Marjan Cugmas
PhD Thesis Menthors: Aleš Žiberna and Anuška Ferligoj. Institution: University of Ljubljana, Faculty of Social Sciences. Year: 2019.

Abstract

Social scientists often seek to understand the relationship between micro social mechanisms and macro social output. In the context of social networks, different micro social mechanisms are usually operationalized by local network mechanisms, while macro social outputs are operationalized by global network structures (Stadtfeld, 2018). Therefore, the aim of this dissertation is to study the relationship between local network mechanisms and global network structures. Not only is the emergence of the selected global network structures addressed, but so too is the transition from one global network structure to another.

Moreno was one of the earliest social network scientists to study global structures of observed networks (Moreno, 1934). By considering the nodes’ attributes and using structured interviews, he explained the social mechanisms responsible for the emergence of the observed global network structures. Later, researchers (Cartwright & Harary, 1956; Davis, 1967; Davis & Leinhardt, 1967; Heider, 1946; Johnsen, 1985) proposed several models for global network structures. Perhaps one of the most popular is the balance model (Cartwright & Harary, 1956), which consists of two clusters of nodes which are internally linked with positive ties and the nodes from different clusters are not linked or they are linked by negative ties. By considering the appearance of different triad types, Davis & Leinhardt (1967) proposed an approach for testing the existence of a selected global network structure in an empirical network.

In this study, a blockmodel is used to define a global network structure. A blockmodel is defined as a network in which the nodes represent clusters of equivalent nodes (according to the structure of their links) from the studied network, while the links in a blockmodel represent the relationships between and within the clusters. The term “block” refers to a submatrix in an adjacency matrix that shows the relationships between nodes from two different clusters or between nodes from the same cluster (Doreian, Batagelj, & Ferligoj, 2005). In this way, a blockmodel can be a very exact representation of a chosen type of global network structure and is used widely across many scientific fields. The blockmodel types considered in this dissertation are the most commonly studied blockmodel types: cohesive blockmodel, (symmetric and asymmetric) core-periphery blockmodel, hierarchical blockmodel, hierarchical-cohesive blockmodel, transitivity blockmodel and transitive-cohesive blockmodel.

Moreover, the social (network) mechanisms can be defined in different ways. Common to the various definitions of social (network) mechanisms is the claim that social mechanisms hold a very important explanatory role (Hedström & Swedberg, 1998). Hedström & Swedberg (1998, p. 7) summarized Schelling (1998) when saying that a “social mechanism can be seen as a systematic set of statements that provide a plausible account on how input and output are linked to one another”. Therefore, social mechanisms may be seen as “models of interaction among individuals that generate the particular social structures” (Gambetta, 1998, p. 102). According to Hedström (2005, p. 25), a social mechanism “describes a constellation of entities and activities that are organized such that they regularly bring about a particular type of outcome”. In the context of social networks, the (macro) social outcome can be operationalized by the global network structure, while the local network mechanisms can be operationalized in different ways, according to their type. Stadtfeld (2018) and Hedström & Swedberg (1998) defined, based on Coleman’s macro-micro-macro model (Coleman (1986)), three types of mechanisms: situational mechanisms (related to the global network structure’s impact on, e.g. the beliefs, desires and opportunities of an individual, action-formation mechanisms (associated with the impact of individuals’ beliefs, desires and opportunities on their actions/behaviour) and transformational mechanisms (related to the impact of individuals’ actions on the global network structure). In this study, the main focus is given to the last two types of local network mechanisms. When Stochastic Actor Oriented Models (SAOM) are used, these types of local network mechanisms are defined through the selected local network statistics, whereas in the case of algorithms from the family of the Network Evolution Models (NEM) (Toivonen et al., 2009) the local network mechanisms are often defined through a set of “if-then” rules.

Even though many studies use the blockmodeling approach to describe the global network structures of the networks observed and many studies rely on Exponential Random Graph Models (ERGM) or SAOM to explain the dynamics and underling mechanisms of the network dynamics, there is no systematic study focusing on the relationship between selected local network mechanisms and selected global network structures, as operationalized by blockmodels. Providing the framework for studying this phenomenon is one aim of this dissertation.

The dissertation consists of two parts. The ability to generate networks with the selected blockmodel types, by considering only the triad types, is addressed in the first part. This research question is especially important because (although the correlation between the number of different triad types and the presence of a given global network structure is well known and generally used) there is no known systematic study addressing a relationship between different triad types and blockmodels as the operationalization of global network structures. Whether the selected blockmodel types can be generated by considering only the triad types without any nodes’ attributes shows that these blockmodels can emerge as a consequence of local network mechanisms such as popularity, assortativity, different transitivity-related mechanisms and others.

To study the mentioned research question, different triad types are classified in the set of allowed and the set of forbidden triad types for each blockmodel type that is considered. A given triad type is called ‘allowed’ if its frequency in a given ideal blockmodel (without any inconsistency) is higher than 0; otherwise, it is called ‘forbidden’. Based on the A-measure (defined as a ratio between the number of triads of the selected type in a network with a given blockmodel and the expected number of triads in a random network with the same density), the sets of allowed and forbidden triad types are further reduced to a set of selected allowed triad types and to a set of selected forbidden triad types.

Two algorithms are used to generate the networks. The first is the proposed Relocating Links algorithm (RL algorithm) while the second is the Markov Chain Monte Carlo algorithm (MCMC algorithm) as implemented in the “ergm” package (Hunter, Handcock, Butts, Goodreau, & Morris, 2008) for the R programming language (Team, 2000). The two different algorithms are used to reduce the possibility of being unable to generate networks with a given blockmodel type due to the characteristics of the algorithm. The RL algorithm is more deterministic than the MCMC algorithm and the RL algorithm requires the exact distribution of triad types for the selected blockmodel whereas the coefficients in MCMC algorithms are arbitrarily set to 2 (for allowed triad types) and -2 (for forbidden triad types).

Several networks are generated by considering each set of triads and each blockmodel type. The level of inconsistencies is evaluated by the proposed Mean Improvement Value (MIV), which allows the fit of a selected (ideal) blockmodel type to be compared against blockmodels of different generated networks.

In general, most studied blockmodels can be generated by only considering different triad types. This shows that some global network structures can emerge by virtue of the local network mechanisms that does not include the nodes’ attributes. Blockmodels generated by considering only the list of forbidden triad types do not have a much higher amount of inconsistencies than networks generated by considering all triad types. This is important to note because the frequencies of the allowed triad types (which is taken into account when the RL algorithm is used to generate networks) contain information on the number of clusters, their size, and the size of the network. However, this is not the case with the forbidden triad types where a researcher must provide only the information regarding which triad types should not appear in the network rather than the frequency of each triad type.

While there is a small number of inconsistencies in the networks generated with most blockmodel types compared to the ideal blockmodel type, it is harder to generate networks with a hierarchical blockmodel. Considering some other local network structures, such as paths of length three, considerably reduces the number of inconsistencies in the blockmodels generated.

The second part of the dissertation considers local network mechanisms, instead of local network structures, in the context of different blockmodel types. While local network structures are represented by different types of subgraphs, the local network mechanisms are processes that drive the specific actions of the nodes in the network, as described above. Different local network mechanisms are operationalized using different network statistics, which are considered by the nodes, when they obtain an opportunity to change the status of their links. This is done by different proposed algorithms from the NEM family, which rely on the following logic: at each iteration of the NEM algorithm, a node is randomly selected. Then, by considering selected node i and all other nodes, different local network statistics are calculated by considering the selected local network mechanisms. These statistics are weighted to enable the different levels of importance of the selected local network mechanisms to be considered. Based on these weighted local network statistics, the selected node creates a link, dissolves or confirms an already existing link. The proposed NEM algorithms mainly differ with respect to how the symmetric links are considered, the way in which the duration of links is considered, and whether newcomers and outgoers are present.

In this study, the mechanisms’ weights are randomly generated. For each set of weights, several networks are generated by using the proposed NEM algorithm while the global network structures are evaluated by the number of inconsistent blocks (Žnidaršič, Ferligoj, & Doreian, 2012, 2017, 2018) and the value of the proposed Relative Fit function (RF), which quantifies the level of inconsistencies in a generated blockmodel according to the ideal blockmodel type.

Given that there are many possible blockmodel types and possible local network mechanisms, the social context of the study is taken into account to select the most relevant blockmodel types and corresponding local network mechanisms. Two such social contexts considered in this dissertation are: (i) friendships and likings among pre-schoolers; and (ii) the flow of knowledge among employees of an international, knowledge-based company. Based on these two social contexts, two blockmodel types are proposed: an (symmetric and asymmetric) core-cohesive blockmodel, and a hierarchical-cohesive blockmodel with last non-cohesive group.

The first blockmodel type consists of at least three groups of nodes, where one group is called the core group and the other groups are called cohesive groups. In networks without inconsistencies, the nodes within all groups are internally all linked to each other. In both the symmetric and asymmetric case, all the nodes from cohesive groups are linked to all the nodes from the core group while only in the symmetric case the core nodes are also linked to the cohesive ones. The latter, a hierarchical-cohesive blockmodel with the last non-cohesive group, is similar to the well-known hierarchical-cohesive blockmodel where the clusters are hierarchically ordered and the nodes within all clusters are linked, but with the proposed blockmodel the nodes from the cluster on the lowest hierarchical level are not linked to each other. It is shown that the symmetric core-cohesive blockmodel type and the hierarchical-cohesive blockmodel with the last non-cohesive group are appropriate to be considered in the social context relating to a kindergarten and a company.

The results of the Monte Carlo simulations show that the symmetric and asymmetric core-cohesive blockmodel types can emerge due to the mutuality, popularity, assortativity (of in-degree) and transitivity-related local network mechanisms when the initial global network structure is an empty network, a network with a cohesive blockmodel, or a network with an asymmetric core-periphery blockmodel. Observations have revealed that some intermediate blockmodel types can emerge during the evolutionary process of generating the chosen blockmodel type.

It was also shown (based on empirical data collected within a larger longitudinal study in the USA and analysed by several researchers, e.g. Schaefer et al. (2010) and DeLay et al. (2016)) that the symmetric core-cohesive blockmodel type appears in interactional networks among pre-schoolers. The fact this blockmodel type can be generated by the selected local network mechanisms does not imply that the global network structures of the empirical networks emerged due to the studied local network mechanisms. However, the appearance of this blockmodel type in the empirical data raises some very important developmental questions, which should be answered by considering the nodes’ attributes. Some of these questions include whether differences exist in some psychological and other types of characteristics (e.g. gender, level of extroversion) between children from the core group and those from the cohesive groups, and whether such a global network structure should be encouraged among pre-schoolers or not.

The same methodology was used to generate the other selected blockmodel types. By considering the selected mechanisms, cohesive, (symmetric and asymmetric) core-periphery and transitive blockmodels can also be generated, but not a hierarchical blockmodel, hierarchical-cohesive blockmodel or transitive-cohesive blockmodel.

A hierarchical-cohesive blockmodel with the last non-cohesive group can emerge as a result of so-called value-related mechanisms (i.e. hierarchical position of the alter, tenure of the alter, popularity level of the alter, the number of partners shared by the ego and the alter) and cost-related mechanisms (i.e. difference in hierarchical position between the ego and the alter, difference in tenure between the ego and the alter, distance between the ego and the alter, the number of partners shared by the ego and the alter). Value and cost are defined through the ego's perception of the costs of obtaining the alter's knowledge and the value of the knowledge so obtained (Nebus, 2006). This blockmodel type can also emerge when newcomers and outgoers are considered. The ability to generate the global network structure, with local network mechanisms that do not consider the nodes’ attributes (except tenure), indicates that a company can develop policies that lead a knowledge flow towards the desired global structure (if it has one).

The most important contribution of this dissertation is the observation that the most common blockmodel types can be generated by the basic local network mechanisms, without taking the attributes of the nodes into account. However, it is necessary to consider the social context and corresponding constraints on the nodes’ characteristics and their behaviour (Doreian & Conti, 2012) while analysing evolution of the global network in real networks.

Global Structures of Knowledge-Flow Networks and Local Network Mechanisms

Marjan Cugmas, Aleš Žiberna, Miha Škerlavaj and Anuška Ferligoj
Conference Paper Conference: SUNBELT 2019. City: Montreal, Canada. Year: 2019.

Abstract

The presentation addresses the global network structure of knowledge-flow networks. A knowledge-flow network operationalizes exchanging knowledge among employees. Therefore, actors in the network represent employees and ties represent receiving different kind of knowledge.

The aim of the presentation is to identify global network structures in the empirical knowledgeflow networks, to define the desired global network structure and to discuss the local network mechanisms that drive the global network structure towards the desired one. Understanding patterns and underlying mechanisms of exchanging knowledge among employees is crucial to ensure competitiveness of a company and to improve the performance and the development of employees.

Blockmodeling is applied on the empirical networks to identify the global network structure. We collected the data within a middle size knowledge-based company in Slovenia at three time points between 2004 and 2007. The evolution of the global network structures is described and the desired blockmodel type for knowledge-flow networks is defined based on the findings from the empirical network data and based on the previous studies on knowledge-flow networks. To discuss the potential local network mechanisms, the algorithm for creating and dissolving links is proposed. It considers different local network mechanisms mainly selected based on the previous studies on the emergence and dynamics of the knowledge-flow networks. Such mechanisms are popularity of the employees, their hierarchical position, the network distance between two employees, transitivity, tenure and others. The global network structures of the generated networks are compared to the desired ones.

The emergence of core-cohesive peripheries blockmodel type

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: COSTNET17. City: Palma de Mallorca, Spain. Year: 2017.

Abstract

The study proposes the core-cohesive peripheries blockmodel type, consisting of one highly popular group of units and two or more cohesive groups of units. Based on the previous studies, regarding friendship networks of preschool childrens, the popularity and transitivity mechanisms are assumed to be related with the emergence of the core-cohesive peripheries blockmodel type. Therefore, two main hypotheses are tested: (i.) the core-cohesive peripheries blockmodel can emerges from random network by the influence of popularity and transitivity mechanisms, and (ii.) the core-cohesive peripheries blockmodel can emerges from random network through core-periphery, since the strength of the popularity and transitivity is assumed not to be constant in time. The hypotheses are tested using the Monte Carlo simulations. The relative criterion function is used to compare the fits of different blockmodel types on empirically generated networks.

Comparing two partitions of non-equal sets of units

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: CEN ISBS 2017. City: Vienna, Austria. Year: 2017.

Abstract

Rand (1971) proposed what has since become a well-known index for comparing two partitions obtained on the same set of units. The index takes a value on the interval between 0 and 1, where a higher value indicates more similar partitions. Sometimes, e.g. when the units are observed in two time periods, the splitting and merging of clusters should be considered differently, according to the operationalization of the stability of clusters. The Rand Index is symmetric in the sense that both the splitting and merging of clusters lower the value of the index. In such a non-symmetric case, one of the Wallace indexes (Wallace 1983) can be used. Further, there are several cases when one wants to compare two partitions obtained on different sets of units, where the intersection of these sets of units is a non-empty set of units. In this instance, the new units and units which leave the clusters from the first partition can be considered as a factor lowering the value of the index. Therefore, a modified Rand index is presented. Because the splitting and merging of clusters have to be considered differently in some situations, an asymmetric modified Wallace Index is also proposed. For all presented indices, the correction for chance is described, which allows different values of a selected index to be compared.

Symmetric core-cohesive blockmodel in an interactional pre-school networks

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: COSTNET18. City: Warsaw, Poland. Year: 2018.

Abstract

The symmetric core-cohesive blockmodel is proposed. A blockmodel is a network where the units are clusters of equivalent (according to the structure of the links) units from the studied network. The term block, in the context of blockmodels, refers to a submatrix showing the links between two clusters. The symmetric core-cohesive blockmodel consists of three or more clusters. The units from each cluster are internally well linked while those from different clusters are ideally not linked to each other. The exception are the units from so called core cluster. These units have a mutual links to all the units in the network. The other clusters are called cohesive clusters.The presentation addresses the question of whether the symmetric core-cohesive blockmodel can be found in interactional pre-school networks. To this aim, the data collected among pre-school children in Head Start preschools (United States, data collected in 2005 and 2006) are analysed. The Monte Carlo simulations are used to confirm that the selected social mechanisms (e.g., popularity, transitivity, mutuality, assortativity), defined on the local network level, can lead to the symmetric core-cohesive blockmodel global structure.

The emergence of the core-cohesive blockmodel

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: Applied Statistics 2018. City: Ribno, Slovenia. Year: 2018.

Abstract

The core-cohesive blockmodel will be proposed in this talk. A blockmodel is one way of representing a global network structure. It is a network where the units are clusters of equivalent units from the studied network and the ties between the clusters are determined by the ties between units of two clusters. The proposed core-cohesive blockmodel type consists of one highly popular cluster and two or more cohesive clusters. The units are internally well connected in each cluster. The units belonging to the cohesive clusters are also linked to the units from the popular one.

Based on the previous studies on the network evolution, it is hypothesized that the popularity, transitivity, assortativity and mutuality mechanisms are related with the emergence of the proposed blockmodel. Therefore, the following research question will be discussed: can the core-cohesive blockmodel type emerges when subjected to the listed mechanisms? The Monte Carlo simulations are applied to this aim. Specifically, network evolution model will be used to generate networks while generalized blockmodeling will be used to assess the global network structure.

The emergence of a symmetric core-cohesive blockmodel type in interactional networks in kindergarten

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: Networks in the Global World 2018. City: Saint Petersburg, Russia. Year: 2018.

Abstract

The presentation addresses the emergence of a global network structure in kindergarten. The global network structure is defined with a blockmodel (a blockmodel is a network where the units are clusters of equivalent units from the studied network). The presentation consists of two parts. In the first part of the presentation, it is evaluated if the global network structure in an empirical interactional networks might be the symmetric core-cohesive blockmodel type. The symmetric core-cohesive blockmodel type consist of one group of units which are linked to all the other units in the network (popular group) and several cohesive groups of units which are internally linked to each other but they are also linked to the popular group. Using the Monte Carlo simulations, the question of whether the well-known mechanisms (popularity, transitivity and assortativity) can lead towards the symmetric core-cohesive blockmodel type (from random network) is addressed in the second part of the presentation.

Popularity, assortativity and transitivity mechanisms and the asymmetric core-cohesive blockmodel type

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Conference Paper Conference: SUNBELT 2018. City: Utrecht, Netherlands. Year: 2018.

Abstract

A blockmodel is a network where the units are groups of equivalent units (regarding their links) from the studied network. In this talk, a new blockmodel type asymmetric core-cohesive will be proposed. This blockmodel type consists of at least three groups of units. The units from all the groups are internally linked to each other. However, a group of units to which all the others are linked (called core group or popular group) also exists. The units from the other clusters (called cohesive) are not linked. It is assumed, but not empirically confirmed, that such blockmodel type can appear in the networks of friendships among children in a pre-school class. Based on the previous studies on the evolution of such networks, the three important mechanisms are identified: the relative popularity, the transitivity and the assortativity in terms of a node's in-degree. The study addresses the question of whether the listed mechanisms can lead the global network structure towards the proposed blockmodel type. To this aim, the Monte Carlo simulations were employed. The results show that the proposed blockmodel type can appear as the consequence of the listed mechanisms, yet the global network structure is even closer to the proposed blockmodel type if the strengths of the selected mechanisms are considered to be variable in time.

Generating random networks with a given blockmodel structure

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Conference Paper Conference: SUNBELT 2017. City: Beijing, China. Year: 2017.

Abstract

The presentation addresses the question of generating networks with a given global structure, where different global structures are defined by selected blockmodels (Wasserman and Faust 1994, Doreian et al. 2005), e.g., cohesive, core-periphery (symmetric and asymmetric), hierarchical (with and without complete blocks on the diagonal) and transitivity (with and without complete blocks on the diagonal). The networks with the given blockmodels are generated using two methods: (i.) the method of relocating of links and (ii.) the less deterministic Monte Carlo Multi Chain algorithm implemented in “ergm” package in R. Different models to generate such networks by considering triads (e.g., all existing types of triads, all allowed or all forbidden types of triads for a given blockmodel) are proposed and evaluated.

Generating random networks with a given blockmodel structure by considering triads and other local network structures

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Conference Paper Conference: ARS'17. City: Naples, Italy. Year: 2017.

Abstract

Based on many empirical observations and theories about social processes, several types of global structures were defined over the last 50 years by, e.g., Cartwright and Harary (1956), Davis (1967), Holland and Leinhardt (1971). The list of all allowed and forbidden types of triads for each global network structure was also proposed. Based on this, one can test the hypothesis regarding the global network structure. The presentation addresses the question of generating networks with a given global structure, where different global structures are defined by different blockmodels (Wasserman and Faust 1994, Doreian et al. 2005). To check whether only considered triads are sufficient to generate the networks with a given blockmodels, two methods are used: the method of relocating of links (RL method) and less deterministic Monte Carlo Multi Chain algorithm (MCMC algorithm) implemented in Exponential Random Graph Modeling (ERGM) R package. It can be shown that considering only different types of triads is enough to generate networks according to the most of analyzed types of blockmodels. Yet this is not true for hierarchical blockmodel structure without complete blocks on the diagonal where additional restrictions are needed.

Factors driving the network to a certain blockmodel type

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Conference Paper Conference: COSTNET Conference. City: Ribno, Slovenia. Year: 2016.

Abstract

The global structure of a network can be described by a blockmodel. There are four basic and most common blockmodels’ types: cohesive, core-periphery, hierarchy and transitivity; with some special cases such as asymmetric core-periphery and transitivity with ties between the units on the same level. On the other hand, the structure of a particular network can be described by some local network characteristics such as the distribution of different types of triangles, shared partners and other statistics. It is known that one could easily discriminate between the global structures, considering local characteristics, in the case when there are no errors in analyzed networks with a specific blockmodel structure. The current presentation will highlight the relationship between several local network characteristics and different amounts of errors in networks with different types of blockmodels.

Measuring the Stability of Co-authorship Blockmodels in Time

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: Data Science and Social Research. City: Naples, Italy. Year: 2016.

Abstract

Kronegger et al (2011) studied the co-authorship networks of four scientific disciplines in Slovenia and identified the most typical collaboration structure as having three basic positions: multi—core, semi—periphery and periphery. Cugmas et al (2015) confirm the assumed structure being present in all Slovenian scientific disciplines and furthermore addressed the question of the stability of obtained cores in the natural and technical sciences on one hand and the social sciences and humanities on the other.
The presentation addresses the measurement of the stability of obtained cores assuming different operationalization of the stability of cores. Therefore, several adopted Rand and Wallace indices are presented and compared based on empirical co-authorship networks of some selected Slovenian scientific disciplines in two time periods.

Stability of co-authorship networks in time

Marjan Cugmas, Luka Kronegger and Anuška Ferligoj
Conference Paper Conference: SUNBELT, International Network for Social Network Analysis. City: Brighton, UK. Year: 2015.

Abstract

Recently, many studies have been performed on scientific collaboration, which is usually operationalised through co-authorship and studied by methods of social network analysis. The starting point of the presented analyses is the work of Kronegger et al. (2011) who confirmed the hypothesis of the multi-core–semi-periphery–periphery structure of a co-authorship network. The presentation addresses the measurement and explanation of the stability of cores, obtained by pre-specified blockmodeling on almost all Slovenian scientific disciplines in two time periods (1991–2000 and 2001–2010). Further, the stability of the obtained cores was measured by the proposed Modified Adjusted Rand Index 1 (MARI 1). Differences between scientific fields, controlled for some characteristics of the co-authorship network and blockmodels, were tested using linear regression.

Different operationalisations of the stability of the co-authorship blockmodels in time

Marjan Cugmas, Anuška Ferligoj and Luka Kronegger
Conference Paper Conference: SUNBELT, International Network for Social Network Analysis. City: Newport Beach, CA. Year: 2016.

Abstract

Cugmas et al (2015) studied the structure of the co-authorship networks of all scientific disciplines in Slovenia. They identified the typical blockmodels’ collaboration structure as multi-core–semi-periphery–periphery. Furthermore, they tested the hypotheses regarding the differences in the stability of obtained cores between the natural and technical sciences and the social sciences and humanities.
The presentation discusses the measurement of the stability of obtained cores under different operationalization of the stability of cores. Therefore, several adopted indices for comparing two partitions (on the same and on the different sets of units) are presented and compared based on empirical co-authorship networks of some selected Slovenian scientific disciplines in two time periods.

On comparing partitions

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: IFCS International Federation of Classification societies. City: Bologna, Italy. Year: 2015.

Abstract

Rand (1971) proposed the Rand Index to measure the stability of two partitions of one set of units. Hubert and Arabie (1985) corrected the Rand Index for chance (Adjusted Rand Index). In this paper, we present some alternative indices. The proposed indices do not assume one set of units for two partitions. Here, one set of units can be a subset of the other set of units. According to the purpose of the comparison of two partitions, the merging and splitting of clusters in two partitions can have different impact on the value of the indices. Therefore, we proposed different modified Rand Indices.

Co-authorship structures of researchers in scientific disciplines in time

Marjan Cugmas, Anuška Ferligoj and Luka Kronegger
Conference Paper Conference: 11th Applied Statistics 2014. Statistical Society of Slovenia. City: Ribno, Slovenia. Year: 2014.

Abstract

The scientific collaboration networks of Slovenian researchers at the level of scientific disciplines during two ten-year time periods (from 1991 to 2000 and from 2001 to 2010) are studied. The collaboration is defined as co-authorship of one or more published outputs that Slovenian Research Agency (ARRS) evaluates as scientific works.
The analysis is based on the work of Kronegger et al (2011), who studied the co-authorship networks of four scientific disciplines in Slovenia and proposed the most typical form of collaboration structure that consists of multi core - semi-periphery - periphery. Based on their study, we applied pre-specified blockmodeling to the most of the scientific disciplines (we excluded those disciplines with too small number of the researchers in them). In the presentation we will discuss the problem of determining the optimal number of clusters and the local optimization problem to determine structurally equivalent clusters. We will graphically present the dynamics of the collaborating groups over time obtained by the blockmodeling procedure.
To measure the transitions between two time periods or the stability of obtained clusterings we used Adopted Rand Index. To explain the obtained transitions by the characteristics of the co-authorship networks (e.g., the number of researchers in the discipline, average number of co-authors of the researchers in the discipline, the rate of change of the number of researchers, the rate of change of density of the network), the characteristics of the obtained block structures (e.g., the number of core clusters, the proportion of the periphery, the number of bridging cores) and the characteristics of the disciplines will be used.

Stability of co-authorship blockmodeling structure in time

Luka Kronegger, Anuška Ferligoj and Marjan Cugmas
Conference Paper Conference: 11th Applied Statistics 2014. Statistical Society of Slovenia. City: Ribno, Slovenia. Year: 2014.

Abstract

Co-authorship as form of scientific collaboration presents the major interaction mechanism between actors at the micro-level of individual scientists. Wide range of mechanisms fostering collaboration produce different structures within general network. The dynamic nature of co-authorship networks presents an interesting problem when trying to analyze the properties of established, emerging and dissolving groups of co-authoring researchers in time.
To analyze the properties of structure dynamics we used blockmodeling method (structural equivalence) with following of individual researchers through time (Kronegger et. al 2011), and stochastic actor based modeling of network dynamics (Siena). In Siena we used two approaches to modeling the effect of structural equivalence to formation of ties within the network: i) including the “balance effect” (Ripley et. al 2013) which is included in predefined set of Siena effects and ii) including the information on structural equivalence on dyadic level using dissimilarity matrix as explanatory variable.
In our research we observed and compared collaborative structures in complete longitudinal co-authorship networks for selected disciplines. Dataset gathered from national bibliographic system COBISS, spanning from 1996 to 2010, was split into three consecutive five-year intervals.

Comparing partitions

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: 12th Applied Statistics 2015. Statistical Society of Slovenia. City: Ribno, Slovenia. Year: 2015.

Abstract

The Rand Index (Rand 1971) is one of the most commonly used indices for measuring the stability of two partitions of one set of units. In some cases, there is a need to compare two partitions obtained on two sets of units, where one set is a subset of another set of units. The merging and splitting of clusters can have different impacts on the value of the indices when comparing two partitions. Therefore, we propose different modified Rand Indices. In addition, we also suggest the adjustment for chance for all proposed indices, which can be obtained by simulations. Some examples of comparing partitions obtained on different sets of units is also given.

Use of SAOM for modelling of network structure stability

Luka Kronegger, Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: 12th Applied Statistics 2015. Statistical Society of Slovenia. City: Ribno, Slovenia. Year: 2015.

Abstract

In presented analysis we made a step closer towards combining two methodological approachies of social network analysis: well established method of blockmodeling based on works of Lorrain & White (1971) and Doreian et al. (2005), and relatively new approaches to stochastic actor based modeling of network dynamincs presented by Snijders (2001, 2005) and Snijders et al. (2007, 2010). Combination of two methods offers a great opportunity for analysis of influence of individual and group characteristics on the dynamics of emergent structure in the network. Presented analysis is performed on data of collaboration networks of Slovenian researchers measured in period from 1996-2010, sliced in to two consecutive 10-year time spans.

Revealing the Blockmodels’ Structure Using the Exponential Random Graph Modeling

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Conference Paper Conference: 13th Applied Statistics 2016. Statistical Society of Slovenia. City: Ribno, Slovenia. Year: 2016.

Abstract

Blockmodeling, as a method to reduce a large and potentially incoherent networks to a smaller and less complex networks (Doreian et al. 2005), differ from community detection methods since blockmodeling allows not only to detect highly connected groups of units, but also the relations between the obtained group of units (de Nooy et al. 2011). Therefore, blockmodeling is seen as appropriate method to describe the global structure of a certain network. The most known structures are cohesive, center-periphery, hierarchy and transitivity (Doreian et al. 2005).

The micro-level processes that might drive the evolution of a network towards a given blockmodel are studied. To this aim, the Exponential Random Graph Modeling is used. The addressed research objective is especially important in the context of studying the evolution of different types of networks.

Stability of co-authorship blockmodels

Marjan Cugmas, Anuška Ferligoj and Luka Kronegger
Conference Paper Conference: ARS'15 International Workshop and ARS'15 Short Course. City: Capri, Italy. Year: 2015.

The abstract is temporarily unavailable

Comparing Partitions from Non-equal Sets of Units

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: Young Statisticians Meeting. City: Vorau, Austria. Year: 2015.

Abstract

Rand (1971) proposed well-known index for comparing two partitions obtained on the same set of units. The index takes the value on the interval between 0 and 1, where a higher value indicates more similar partitions. The index is symmetric in the sense that both splitting and merging of clusters lower the value of the index. Sometimes, e.g. when the units are observed in two time periods, the splitting and merging of clusters should be considered differently, according to the operationalization of stability of clusters. In that case the Wallace index B' (Wallace 1983) can be used. Furthermore, there are several cases when one would want to compare two partitions obtained on the different sets of units, where one is a subset of another. In that case, the new units and units which leave the clusters from the first partition can be considered as a factor lowering the value of the index. Therefore, two modified Rand indices will be presented, along with its correction for chance, which allow comparing different values.

The implications of peer network structure: Considering peer network structure creation and influence on adolescent development

Marjan Cugmas, Aleš Žiberna, Anuška Ferligoj and Dawn DeLay
Conference Paper Conference: SRA (Society for Research on Adolescence) Biennial Meeting. City: Minneapolis, Minnesota. Year: 2018.

Abstract

Research aimed at understanding the dynamics of peer relationships must consider two important points: (1) the complexity of interpersonal relationship dynamics and (2) the complexity of structural constraints, such as classrooms and schools, on peer relationship dynamics. Such investigations also present statistical challenges that require the application of innovative methodologies, including data simulation, multilevel modeling, and social network analysis. Thus, this symposium aims to discuss some critical methodological considerations, as well as real world implications for the role of peer network structure in child and adolescent development.
To this end, three papers will be presented that describe how developmental scholars might think about and conceptualize peer network structures using advanced methodological techniques (e.g., simulation, multilevel, social network analysis) in order to address important developmental questions (e.g., bullying, helping behavior). Three presentations from international scholars in the Netherlands, Slovenia, and the USA make up this symposium. The first presentation describes the dynamics behind the creation of peer network structure using simulated social network data. The second presentation builds upon this study by considering how multilevel models can be used to understand the impact of peer network structure at the individual and classroom level, as it relates to important developmental outcomes (e.g., bullying). The third presentation discusses the need to consider multiple and overlapping interactions between specific forms of social network structures (e.g., friendship and helping networks). Discussions consider the significant role of developing peer network structures throughout childhood and adolescence.

Generiranje globalnih struktur z različnimi vrstami triad

Marjan Cugmas
Conference Paper Conference: NetSlo'18. City: Ljubljana, Slovenia. Year: 2018.

Abstract

Predstavitev naslavlja vprašanje zmožnosti generiranja omrežij s točno določeno globalno strukturo zgolj z upoštevanjem lokalnih podstruktur. Različne globalne strukture omrežij so operacionalizirane z različnimi vrstami bločnih modelov. Bločni model je omrežje, kjer so enote skupine enakovrednih enot opazovanega omrežja. Pri tem se omejimo na strukturno enakovrednost (dve enoti sta strukturno nakovredni, če sta enako povezani z ostalimi enotami). V analizi preučujemo najbolj znane vrste bločnih modelov: koheziven, center-periferija, tranzitiven in hierarhičen tip bločnega modela. Lokalne strukture omrežij predstavljajo različne vrste triad. Za generiranje omrežij sta uporabljena algoritem prestavljanja povezav in Monte Carlo Multi Chain algoritem, implementiran v programski paketek »ergm« programskega jezika R. Rezultati kažejo, da je, zgolj z upoštevanjem različnih vrst triad, mogoče generirati omrežja različnih globalnih struktur, a vključitev dodatnih lokalnih struktur (na primer poti dolžine tri) lahko znatno pripomore k nastanku želene globalne strukture. Pri generiranju tovrstnih omrežij ne upoštevamo lastnosti enot.

Comparing two partitions obtained on different sets of units

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: International Statistical Conference in Croatia (ISCCRO’16) City: Zagreb, Croatia. Year: 2016.

Abstract

Rand Index (Rand 1971) is used to compare two partitions obtained on the same sets of units, where merging and splitting of clusters are seen as factors which lower the value of the index (the index can take the value on the interval between 0 and 1 where higher value indicates more similar partitions). In some research problems, the splitting and merging of clusters have to be considered as factors with different effects on the value of an index. In such cases one of the Wallace indices can be used (Wallace 1983). Here only the merging or only the splitting of groups lowers the value of an index. The presentation addresses the case when two partitions are obtained on two different sets of units with a non-empty intersection (e.g., when the sets of units are obtained in two different time points). In such cases the in-coming and out-going units are usually present and considered as factors which indicates lower level of stability (or similarity) of two partitions. Therefore, the two modified Rand indices and two Wallace indices are presented along with the correction for chance, which enables to compare the values of indices obtained on different partitions.

Measuring stability of co-authorship structures in time

Marjan Cugmas and Anuška Ferligoj
Conference Paper Conference: 48th Scientific Meeting of the Italian Statistical Society (SIS2016) City: Salerno, Italy. Year: 2016.

Abstract

Kronegger et al (2011) studied the co-authorship networks of four scientific disciplines in Slovenia and identified the most typical collaboration structure as having three basic positions: multi—core, semi—periphery and periphery. Cugmas et al (2015) confirmed the assumed structure being present in all Slovenian scientific disciplines and furthermore addressed the question of the stability of obtained cores. The presentation addresses the measurement of the stability of obtained cores assuming different operationalization of the stability of cores. Several adopted Rand and Wallace indices are presented and compared based on empirical co-authorship networks of some selected Slovenian scientific disciplines in two time periods.

Factors changing blockmodels' type in time

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Conference Paper Conference: Second European Conference on Social Networks. City: Paris, France. Year: 2016.

Abstract

"The aim of a blockmodeling is to reduce a large potentially incoherent network to smaller and less complex network (Doreian et al. 2005)". In comparison with community detection methods, blockmodeling allows not only to detect highly connected groups of units, but also the relations between the obtained groups of units (de Nooy et al. 2011). Therefore, blockmodeling is seen as appropriate method to describe the structure of a certain network. The most known structures of blockmodels are center-periphery, hierarchy, cohesion and others (Doreian et al. 2005). Studies done on empirical networks show that the network's structure can move from one to another blockmodel type in time under the in uence of some factors (e.g. the blockmodel of center-periphery type can move to a complete network, where all nodes are linked) (Bettencourt et al 2009, Kronegger et al 2015). The presentation addresses the factors that a ect the transition from one type of a blockmodel to another type of a blockmodel.

Structure and stability of scientific collaboration

Marjan Cugmas, Luka Kronegger, Aleš Žiberna, Franc Mali and Anuška Ferligoj
Invited Lecture Host: Linkoping University. City: Online. Year: 2021.

Abstract

A consensus exists that scientific collaboration must be encouraged since it helps exchange and develop ideas and increase the visibility and quality of scientific output. The policymakers must understand scientific collaboration on different levels to propose efficient incentives for scientific collaboration.

Therefore, the presentation will begin with discussing global structures (in terms of blockmodels) of scientific collaboration and their stability in time on the level of various scientific disciplines. Then, the focus will be narrowed to scientific collaboration among researchers from social sciences. Here, scientific collaboration will be studied simultaneously on the individual level and the organizational level. The obtained global network structures will be visualized and described.

The analyses will be based on the national information systems, containing all researchers and research organizations registered at the Slovenian research agency.

O bločnem modeliranju in o generiranju omrežij z danim bločnim modelom na podlagi triad

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Invited Lecture Host: Faculty of information studies. City: Novo mesto, Slovenia. Year: 2018.

Abstract

Pogovarjali se bomo o zmožnosti generiranja omrežij s točno določeno globalno strukturo - zgolj z upoštevanjem lokalnih podstruktur. Lastnosti enot ne bomo upoštevali.
Različne globalne strukture omrežij bomo operacionalizirali z različnimi vrstami bločnih modelov. Bločni model je omrežje, kjer so enote skupine enakovrednih (glede na strukturo povezav) enot opazovanega omrežja. Za lažjo predstavo o bločnih modelih in bločnem modeliranju, kot postopku za določitev bločnega modela v empiričnih omrežjih, si bomo pogledali nekaj pristopov k bločnemu modeliranju na empiričnih primerih so-avtorskih omrežij. Kot lokalne podstrukture omrežij bomo obravnavali različne vrste triad.
Za generiranje sintetičnih omrežij bomo uporabili algoritem prestavljanja povezav in Monte Carlo Multi Chain algoritem, implementiran v programski paketek "ergm" programskega jezika R. Pokazali bomo, da je mogoče z upoštevanjem različnih vrst triad generirati omrežja različnih globalnih struktur, a vključitev dodatnih lokalnih struktur lahko znatno pripomore k nastanku želene globalne strukture.

Comparing Two Partitions Obtained on Different Sets of Units

Marjan Cugmas and Anuška Ferligoj
Invited Lecture Host: Institute for Biostatistics and Medical Informatics. City: Ljubljana, Slovenia. Year: 2016.

Abstract

Rand Index (Rand 1971) is known as one of the most common indices for comparing two partitions obtained on the same sets of units. It can take the value on the interval between 0 and 1 where higher value indicates more similar partitions. When measuring the similarity of two partitions the splitting and merging of clusters can be considered as factors with different effects on the value of an index. The Rand Index belongs to a group of symmetric indices in this context since both merging and splitting have a negative effect on the value of the measure. When the splitting and merging of groups have to be considered differently - according to the operationalization of studied groups - one of the Wallace indices can be used (Wallace 1983). Here, only the merging or only the splitting of groups lowers the value of an index.
In the case when two partitions are obtained on two different sets of units with a non-empty intersection, the number of in-coming and out-going units (e.g., when the sets of units are obtained in different time points) can be considered as a factors which lowers the value of an index. Therefore the two symmetric modified Rand indices and two asymmetric Wallace indices will be presented along with the correction for chance, which enables to compare the values of indices obtained on different partitions.

Strukture so-avtorskih omrežij slovenskih raziskovalcev in stabilnost raziskovalnih skupin v času

Marjan Cugmas and Anuška Ferligoj
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2015.

Abstract

Bločno modeliranje omogoča reduciranje velikih, nekoherentnih omrežij v manjša in razumljivejša omrežja, ki jih je lažje interpretirati. Na tokratnem sredinem seminarju bomo predstavili rezultate bločnega modeliranja so-avtorskih omrežij slovenskih raziskovalcev v dveh časovnih obdobjih (1991-2000 in 2001-2010) na ravni znanstvenih disciplin, kot jih opredeljuje Javna agencija za raziskovalno dejavnost RS.

Za merjenje stabilnosti skupin raziskovalcev bomo izhajali iz Adjusted Rand Index (ARI), ki se uporablja za primerjanje dveh razvrstitev, izračunanih na isti množici enot. V kontekstu preučevanja so-avtorskih omrežij v dveh časovnih obdobjih, pa enote navadno prihajajo v omrežje (npr. mladi raziskovalci) ali ga zapuščajo (npr. upokojitev), kar pomeni, da je razvrščanje (bločno modeliranje) v prvem in v drugem časovnem obdobju izvedeno na dveh različnih množicah enot. Predstavljene različne prilagoditve ARI-ja omogočajo primerjanje razvrstitev, kjer je ena množica enot za razvrščanje podmnožica druge množice enot. Združevanje in deljenje skupin raziskovalcev prav tako različno vplivata na vrednosti tako prilagojenih ARI-jev.

V zaključku bomo predstavili izračunane vrednosti ene izmed različic prilagojenih ARI-jev za vse analizirane znanstvene discipline.

Generiranje omrežij z izbrano globalno strukturo z uporabo lokalnih podstruktur

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2016.

Abstract

Glede na empirične podatke in različna teoretična izhodišča, so raziskovalci definirali različne tipične globalnih struktur omrežij, na primer model 'ballance' (Cartwright in Harary 1956), model 'clustering' (Davis 1967) in model 'transitivity' (Holland i Leinhardt 1971). Davis in Leinhardt (1967) sta predstavila klasifikacijo vseh možnih tipov grafov velikosti tri in v okviru slednje je nastal seznam prepovedanih in dovoljenih tipov trikotnikov za omenjene globalne strukture. Davis in Leinhardt (1970) sta ugovarjala, da je zaradi možnosti prisotnosti napak v omrežju potreben manj deterministični pristop k ugotavljanju globalnih struktur. Tako sta, na podlagi porazdelitev trikotnikov v slučajih omrežjih, zasnovala teste za preverjanje domnev o številu prepovedanih in dovoljenih tipov trikotnikov v empiričnih omrežjih.

Na tokratnem Sredinem seminarju bomo globalno strukturo omrežij definirali z različnimi tipi bločnih modelov (koheziven, tranzitiven, center-periferija, hierarhičen), poleg različnih tipov trikotnikov pa bomo preučevali tudi nekaj drugih lokalnih značilnosti omrežij. Pokazali bomo, katere statistike, povezane z lokalnimi značilnostmi omrežij so enake 0 v primeru omrežij brez napak in nadalje, kako različni deleži napak v omrežju vplivajo na te statistike. Glede na slednje bomo izbrali tiste lokalne značilnosti omrežij, ki jih je potrebno upoštevati pri generiranju slučajnih omrežij, da bi dobili določeno globalno strukturo omrežja. V okviru tega bomo predstavili dva načina simuliranja omrežij z določeno globalno strukturo: bolj determinističen iterativni postopek s prestavljanjem povezav in, v okviru Exponential Random Graph Modeling (ERGM), manj deterministični Monte Carlo Multi Chain algoritem.

Zgolj na podlagi informacije o prepovedanih tipih trikotnikov (ob predpostavljeni fiksni gostoti) je mogoče generirati skoraj popolna omrežja z različnimi globalnimi strukturami, kar pa ne velja za hierarhični model z več skupinami, kjer so potrebne dodatne omejitve.

Generiranje omrežij z izbrano globalno strukturo z uporabo lokalnih podstruktur, 2. del

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2016.

Abstract

V drugem delu seminarja bomo na hitro ponovili pojme iz prvega dela, ki so potrebni za razumevanje drugega dela. V drugem delu bomo spoznali algoritme za generiranje omrežij z izbrano globalno strukturo.

Glede na analize iz prvega dela bomo izbrali tiste lokalne značilnosti omrežij, ki jih je potrebno upoštevati pri generiranju slučajnih omrežij, da bi dobili določeno globalno strukturo omrežja. V okviru tega bomo predstavili dva načina simuliranja omrežij z določeno globalno strukturo: bolj determinističen iterativni postopek s prestavljanjem povezav in, v okviru Exponential Random Graph Modeling (ERGM), manj deterministični Monte Carlo Multi Chain algoritem.

Zgolj na podlagi informacije o prepovedanih tipih trikotnikov (ob predpostavljeni fiksni gostoti) je mogoče generirati skoraj popolna omrežja z različnimi globalnimi strukturami, kar pa ne velja za hierarhični model z več skupinami, kjer so potrebne dodatne omejitve.

Center-periferija kohezivni tip bločnega modela

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2017.

Abstract

Bločni model je omrežje, kjer so vozlišča skupine enakovrednih enot (glede na povezave z ostalimi enotami). Med bolj znane tipe bločnih modelov sodita kohezivni in center-periferija. Prvi navadno sestoji iz nekaj skupin, ki so znotraj dobro povezane, med enotami iz različnih skupin pa ni povezav. Po drugi strani pa tip center-periferija sestoji iz dveh skupin, kjer so enote iz prve skupine (popularne enote) med sabo dobro povezane, enote iz druge skupine (periferne enote) pa med sabo niso povezane. Periferne enote so povezane s popularnimi enotami.

Na tokratnem sredinem seminarju bomo predstavili bločni model, ki je nekakšna kombinacija zgoraj navedenih tipov bločnih modelov: center-periferija kohezivni tip bločnega modela. Ta sestoji iz ene skupine popularnih enot in več skupin kohezivnih enot. Enote iz kohezivnih skupin so povezane s popularnimi enotami. Na podlagi predhodnih raziskav, s področja razvoja omrežij prijateljstev med otroci v vrtcih, bomo preverili, ali lahko izbrani mehanizmi (popularnost, asortativnost in tranzitivnost) vplivajo na nastanek center-periferija kohezivnega tipa bločnega modela.

Generiranje omrežij z danim bločnim modelom ter razvrstitvijo, upoštevajoč izbrane lokalne mehanizme

Marjan Cugmas and Aleš Žiberna
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2021.

Abstract

Za namene evalvacije različnih pristopov k bločnemu modeliranju časovnih in povezanih omrežij je potrebno generirati sintetična omrežja v več časovnih točkah z danim bločnim modelom in razvrstitvijo. Nadalje je zaželeno pri generiranju takih omrežij upoštevati izbrane lokalne omrežne mehanizme, ki se pojavljajo v empiričnih omrežjih z izbranim bločnim modelom. Na tokratnem sredinem seminarju bomo tako razpravljali o možnostih prilagoditve različnih obstoječih načinov za generiranje omrežij z upoštevanjem lokalnih omrežnih mehanizmov ter o drugih alternativnih, potencialno bolj stohastičnih pristopih.

Kvantitativna analiza najtežjih vprašanj v spletni svetovalnici To sem jaz

Marjan Cugmas
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2021.

Abstract

Na svetovni dan zdravja, 7. aprila 2001, so na Zavodu za zdravstveno varstvo Celje (danes Območni enoti Celje Nacionalnega inštituta za javno zdravje) začeli z izvajanjem preventivnega programa To sem jaz (TSJ), ki je namenjen mladostnikom. V okviru tega koordinirajo preventivni program mladinske spletne svetovalnice (www.tosemjaz.net), od leta 2012 pa tudi sprotno kodirajo vsako prispelo vprašanje. Vprašanja razvrstijo na podlagi šifranta, glede na tipologijo težav. Določijo tudi spol in starost uporabnika. Na tak način so do leta 2020 kodirali že skoraj 17 tisoč vprašanj.

V letu 2019 so razvili on-line orodje TSJ Dashboard za sprotno analizo vsebin v spletni svetovalnici ter za pregled obiskanosti spletne svetovalnice. V prvem delu tokratnega Sredinega seminarja bomo, z uporabo TSJ Dashboard, preverili, kako se z leti spreminja število vprašanj v spletni svetovalnici, kdo so pisci vprašanj (glede na spol in starost), ob katerih urah pošiljajo vprašanja v spletno svetovalnico, pa tudi, katere teme vprašanj se najpogosteje pojavljajo in kako dolga (v smislu dolžine znakov) so vprašanja različnih tem.

V spletni svetovalnici se pojavljajo tudi tako imenovana najtežja vprašanja. To so vprašanja, ki so povezana s samomorilnostjo, depresijo, medvrstniškim nasiljem, samopoškodbami in drugimi stiskami, o katerih mladostniki sporočajo v kriznih situacijah. V spletni svetovalnici je bilo v letih med 2012 in 2017 približno 9 % tovrstnih vprašanj. V drugem delo Sredinega seminarja bodo predstavljeni rezultati analize primerjave vprašanj, ki so opredeljena kot najtežja, ter ostalih vprašanj. V primerjavi se osredotočamo na pojavnost ter dolžino posameznih vrst vprašanj, glede na spol in starost, čas do odgovora, pa tudi na sopojavljanje različnih tem najtežjih vprašanj.

Lahko z uporabo mere relativnega prileganja (RF) učinkovito določimo vrsto bločnega modela in število skupin?

Marjan Cugmas
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2021.

Abstract

Bločni model je omrežje v katerem vozlišča predstavljajo skupine enakovrednih (glede na strukturo povezav) enot iz preučenega omrežja. Izraz blok se nanaša na povezave med dvema skupinama ali povezave znotraj skupine. V primeru posplošenega bločnega modeliranja, vrednost kriterijske funkcije (KF) meri (ne)prileganje empiričnega omrežja (in razvrstitve) izbranemu bločnemu modelu. Ker je vrednost KF odvisna od številnih dejavnikov (na primer velikosti omrežja, gostote), smo predlagali mero relativnega prileganja (RF). Pričakovana vrednost RF v primeru slučajnih omrežij je 0, najvišja vrednost pa je 1 (primer brez neskladnih povezav). Vrednosti RF, dobljene na različnih empiričnih omrežjih so primerljive, zaradi česar se pojavi vprašanje o potencialni uporabnosti RF za izbiro primerne vrste bločnega modela in števila skupin. To vprašanje smo naslovili z uporabo Monte Carlo simulacij, pri katerih smo upoštevali različne vrste bločnih modelov, število skupin in obseg neskladnih povezav. Rezultati kažejo, da je z uporabo RF mogoče izbrati najbolj primeren bločni model in število skupin v primerih, vsaj zadovoljivega prileganja omrežja bločnemu modelu.

Pristopi za bločno modeliranje časovnih omrežij

Aleš Žiberna and Marjan Cugmas
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2021.

Abstract

V družboslovju je metodologija analize omrežij izjemno pomembna pri preučevanju odnosov med enotami (osebami, podjetji, in drugimi), operacionaliziranih z omrežji. Kadar nas zanimajo vzorci odnosov med skupinami enot, lahko uporabimo metodo bločnega modeliranja, s katero identificiramo skupine enakovrednih enot, glede na njihove povezave v omrežju, kakor tudi povezave oziroma odnose med dobljenimi skupinami. Pogosto želimo analizirati pojave v času. V ta namen lahko uporabimo posebne različice bločnega modeliranja, ki so prilagojene za analizo časovnih omrežij in ki upoštevajo odvisnost povezav med enotami v času.

Na tokratnem Sredinem seminarju bo Aleš Žiberna predstavil najnovejše pristope za bločno modeliranje tovrstnih omrežij, tako s področja stohastičnega bločnega modeliranja, kakor tudi k-means bločnega modeliranja.

Marjan Cugmas bo v drugem delu seminarja predstavil rezultate Monte Carlo analiz, s katerimi je preverjal, kako se različne metode bločnega modeliranja časovnih omrežij odnesejo v primerih različno velikih omrežij, različnih vrst bločnih modelov, pa tudi različnih načinov generiranja omrežij (z upoštevanjem nekaterih lokalnih mehanizmov vs. brez upoštevanja lokalnih omrežnih mehanizmov).

Scientific co-authorship networks

Marjan Cugmas, Anuška Ferligoj, Luka Kronegger
Invited Lecture Host: Higher School of Economics, National Research University. City: Moscow, Russia. Year: 2019.

Abstract

In the first part of the presentation, different indices for comparing two partitions are presented (Cugmas, Ferligoj 2018). They are based on the Rand index (Rand 1971) and Wallace indices (Wallace 1983) which are used to compare the stability (or similarity) of two partitions, obtained on the same set of units. In the case of the Rand index merging and splitting of clusters indicate lower stability while in the case of Wallace indices only splitting or only merging of clusters indicates lower stability of clusters. Let us assume that one set of units was observed at the first time point while the second set was observed at the second time point. In this case some units join at the second time point or/and some units leave at the second time point. One has to decide how to consider these units. Therefore, different modifications of Rand index and Wallace indices are proposed. For all indices, the correction for chance is described (this allows different values of a selected index to be compared).

In the second part, the structures of co-authorship networks are examined by using the pre-specified blockmodeling approach (Doreain et al. 2005). The multi-core—semi-periphery—periphery (Kronegger et al. 2011) blockmodel type is described in this presentation and used in the pre-specified blockmodeling. The analyses are done on the co-authorship networks for each scientific discipline as defined by the Slovenian Research Agency. The nodes represent authors and the links between the nodes operationalize co-authorship of at least one scientific bibliographic unit. The data for two time periods are considered (1991–2000 and 2001–2010). Different scientific disciplines are compared regarding the number of authors, the density of the obtained networks, the number of cores, the size of the periphery etc. The obtained co-authorship networks are also visualized in line with the obtained blockmodels.

In the third part of the presentation, the proposed indices are used to measure the stability of the obtained blockmodels. A special attention is given to the stability of the cores. A core is a group of authors which co-author in a more systematic way with each other than with the others in the network. Different factors, which are assumed to affect the stability of cores, are used to analyze the source of (in)stability of scientific disciplines and to explain the differences in the stability of scientific disciplines.

The presentation is based on the chapter Scientific co-authorship networks which will appear in the book Advances in Network Clustering and Blockmodeling (edited by Doreain et al., published by Wiley in 2019).

The structure of scientific collaboration

Marjan Cugmas, Luka Kronegger, Aleš Žiberna, Franc Mali, Anuška Ferligoj
Invited Lecture Host: Higher School of Economics, National Research University. City: Moscow, Russia. Year: 2021.

Abstract

Collaboration is an essential part of scientific work. It helps researchers to exchange and develop ideas, share working tools and materials, and increase the visibility and quality of scientific output. Consequently, there is a consensus that scientific collaboration (SC) should be encouraged, which is reflected in R&D policies on institutional, national, and international levels. To propose and evaluate efficient incentives for SC, one must understand the structure and the social mechanisms of SC. Therefore, the structure of SC among Slovenian researchers will be addressed in this presentation in two parts.

In the first part, we will address global structures and their stability (1991 – 2010) on the level of scientific disciplines. SC will be operationalized by co-authorships of scientific bibliographic items. The global network structures will be described by blockmodels, and the stability of the corresponding clusters of researchers will be measured by the modified adjusted Rand index.

In the second part, we will take a closer look at SC among researchers from the field of social sciences in the period 2005 – 2015. We will simultaneously study SC's structures on the individual level (through co-authorship) and organizational level (through joint research projects among organizations) using the k-means multilevel blockmodeling approach. The obtained global network structures will be visualized and described, considering the Slovenian context of SC.

The analyses will be based on the national information systems SICRIS and COBISS, which contain all researchers and research organizations registered at the Slovenian research agency.

Global network structure and local network mechanisms of knowledge-flow networks

Marjan Cugmas, Aleš Žiberna, Anuška Ferligoj, Miha Škerlavaj, Nada Zupan
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2019.

Abstract

Understanding patterns and underlaying mechanisms of exchanging knowledge among employees is crucial to ensure their professional development and consequently competitiveness of a company. Exchanging knowledge of different types can be operationalized by so called knowledge-flow networks. In such networks, nodes represent employees and links among them are measured by the flow of different kinds of knowledge.

The presentation will consist of two parts. In the first part, the analysis of the data, collected among the employees of a middle size Slovenian company, will be presented (Miha Škerlavaj, 2007). The data were collected at three time points (2004, 2006 and 2007). The generalized blockmodeling (Doreian, Batagelj, & Ferligoj, 2005) was used to reveal the global network structures of the knowledge-flow networks. Then, different types of indices for measuring the similarity of two partitions (Cugmas & Ferligoj, 2018) were used to explain the stability of the obtained blockmodels in time and finally, different attributes (characteristics of the employees, e.g., gender, tenure, …) were considered to describe the mechanisms that might cause the observed dynamics of the global network structure.

The algorithm for generating knowledge-flow networks (by considering different local network mechanisms) will be presented in the second part of the presentation. The algorithm and the corresponding mechanisms are defined based on the theory proposed by Nebus (2006). Here, advice-seekers consider the cost of obtaining advice from a given employee on one hand and the potential value of the employees’ advice on the other hand. Different types of the perceived costs and the perceived values are operationalized by different local network mechanisms. The Monte Carlo simulations were used to test which local network mechanisms are necessary to obtain a hierarchical blockmodel with complete blocks on the diagonal.

Središčno-kohezivni tip bločnega modela v omrežjih interakcij med predšolskimi otroki

Marjan Cugmas, Aleš Žiberna and Anuška Ferligoj
Invited Lecture Host: Faculty of Mathematics and Physics. City: Ljubljana, Slovenia. Year: 2018.

Abstract

Bločni model je omrežje, kjer so vozlišča skupine enakovrednih enot (glede na povezave z ostalimi enotami). Na enem izmed preteklih Sredinih seminarjev smo predstavili tako imenovan (simetričen in asimetričen) središčno-kohezivni tip bločnega modela. Ta sestoji iz skupine popularnih enot in več kohezivnih enot, ki so povezane s popularnimi enotami. Popularne enote so povezane z enotami iz kohezivnih skupin, ko gre za asimetrični tip bločnega modela, poleg slednjega pa so enote iz kohezivnih skupin povezane tudi s popularnimi enotami, ko gre za simetričen tip bločnega modela. Za asimetrično različico smo pokazali, da lahko nastane kot posledica mehanizmov popularnosti, asortativnosti in tranzitivnosti. Ti so pogosto upoštevani pri modeliranju omrežij prijateljstev med predšolskimi otroki.

Na tokratnem sredinem seminarju bomo preverjali, ali je simetričen središčno-koheziven tip bločnega modela prisoten v omrežjih interakcij med otroki v vrtcih. V ta namen bomo analizirali omrežja, ki so bila zbrana med predšolskimi otroki v letih med 2005 in 2008 v Združenih državah Amerike. V takem omrežju sta otroka povezana, če sta bila opažena med skupnim igranjem. Podatki so bili zbrani v okviru večje longitudinalne raziskave, analizirani pa tudi z uporabo SIENA modelov (Schaefer et al. 2010).

The needs and dilemmas in the field of drugs, which adolescents confide to the web consellors on www.tosemjaz.net

Nuša Konec Juričič, Ksenija Lekić, Petra Tratnjek, Marjan Cugmas
Conference Paper Conference: 7th South Eastern European and Adriatic Drug Addiction Treatment Conference and 14th SEEAnet Symposium on Addictive Behaviours and 6. slovenski simpozij o okužbi z virusom hepatitisa C pri osebah, ki uživajo droge. City: Ljubljana, Slovenia. Year: 2015.

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