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Generating global network structures by triad types

Marjan Cugmas, Anuška Ferligoj and Aleš Žiberna
Journal Paper Manuscript submitted to Plos ONE. Also available at arXiv.

Abstract

This paper addresses the question of whether it is possible to 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 method of relocating links; and (ii) the Monte Carlo Multi Chain algorithm implemented in the "ergm" package implemented in R. Although all types of triads can generate networks with the selected blockmodel types, the selection of only a subset of triads improves the generated networks' blockmodel structure. However, 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 on only 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. The book is not published yet. Manuscript available at arXiv.
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).

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.

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.

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.

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.

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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