Andrej Mrvar

Exploratory Social Network Analysis with Pajek: List of Illustrations

This is an extensively revised and expanded second edition of the successful textbook on social network analysis integrating theory, applications, and network analysis using Pajek. The main structural concepts and their applications in social research are introduced with exercises. Pajek software and data sets are available so readers can learn network analysis through application and case studies. Readers will have the knowledge, skill, and tools to apply social network analysis across the social sciences, from anthropology and sociology to business administration and history. This second edition has a new chapter on random network models, for example, scale-free and small-world networks and Monte Carlo simulation; discussion of multiple relations, islands, and matrix multiplication; new structural indices such as eigenvector centrality, degree distribution, and clustering coefficients; new visualization options that include circular layout for partitions and drawing a network geographically as a 3D surface; and using Unicode labels. This new edition also includes instructions on exporting data from Pajek to R software. It offers updated descriptions and screen shots for working with Pajek (version 2.03).

A partitioning approach to structural balance

Abstract The classic formulation of structural balance by Cartwright and Harary (Psychological Review, 63, 1956, 277–293) had the basic structural theorem that a balanced structure could be partitioned into two mutually antagonistic subgroups each having internal solidarity. Davis (Human Relations, 20, 1967, 181–187) extended this theorem for cases where there can be more than two such mutually antagonistic subgroups. We use these theorems to construct a criterion function for a local optimization partitioning procedure for signed digraphs. For any signed digraph, this procedure yields those partitions with the smallest number of errors, a measure of the imbalance in the graph, and an identification of those links inconsistent with both generalized and structural balance. These methods are applied to some artificial data and to the affect data from Sampson (A novitiate in a period of change: An experimental and case study of social relationships, Dissertation, Cornell University, 1968). The latter provides a positive test of a basic tenet of balance theory, that there is a tendency towards balance with signed relations in human groups. While these methods can be applied to all signed digraphs and signed graphs, the balance hypothesis is relevant only for affect ties.

Partitioning signed social networks

Structural balance theory has proven useful for delineating the blockmodel structure of signed social networks. Even so, most of the observed signed networks are not perfectly balanced. One possibility for this is that in examining the dynamics underlying the generation of signed social networks, insufficient attention has been given to other processes and features of signed networks. These include: actors who have positive ties to pairs of actors linked by a negative relation or who belong to two mutually hostile subgroups; some actors that are viewed positively across the network despite the presence of negative ties and subsets of actors with negative ties towards each other. We suggest that instead viewing these situations as violations of structural balance, they can be seen as belonging to other relevant processes we call mediation, differential popularity and internal subgroup hostility. Formalizing these ideas leads to the relaxed structural balance blockmodel as a proper generalization of structural balance blockmodels. Some formal properties concerning the relation between these two models are presented along with the properties of the fitting method proposed for the new blockmodel type. The new method is applied to four empirical data sets where improved fits with more nuanced interpretations are obtained.

A subquadratic triad census algorithm for large sparse networks with small maximum degree

In the paper a subquadratic (O(m), m is the number of arcs) triad census algorithm for large and sparse networks with small maximum degree is presented. The algorithm is implemented in the program Pajek.

Some analyses of Erdős collaboration graph

Abstract Patrick Ion (Mathematical Reviews) and Jerry Grossman (Oakland University) maintain a collection of data on Paul Erdos, his co-authors and their co-authors. These data can be represented by a graph, also called the Erdos collaboration graph. In this paper, some techniques for analysis of large networks (different approaches to identify ‘interesting’ individuals and groups, analysis of internal structure of the main core using pre-specified blockmodeling and hierarchical clustering) and visualizations of their parts, are presented on the case of Erdos collaboration graph, using the program Pajek .

Partitioning approach to visualization of large graphs

The structure of large graphs can be revealed by partitioning graphs to smaller parts, which are easier to handle. In the paper we propose the use of core decomposition as an efficient approach for partitioning large graphs. On the selected subgraphs, computationally more intensive, clustering and blockmodeling can be used to analyze their internal structure. The approach is illustrated by an analysis of Snyder & Kick’s world trade graph.

Intra-Organizational Learning Networks within Knowledge-Intensive Learning Environments

Organizational learning contributes to organizational performance. One research question that remains inadequately explained is how learning occurs. Can it be explained by using the acquisition or participation perspectives? Or is there a need for some other view? This paper suggests that learning networks form an important learning environment for knowledge transfer. A case study of a software development and business consulting company is used to test the network perspective on intra-organizational learning. Both exploratory and confirmatory social network analysis of a learning network within the IT company are used to establish learning patterns within organizations. Learning needs to be seen as both participation in communities of practice and a flow of previously acquired knowledge.

Partitioning large signed two-mode networks: Problems and prospects

Abstract While a substantial amount of attention within social network analysis (SNA) has been given to the study of one-mode networks, there is an increasing consideration of two-mode networks. Recent research on signed networks resulted in the relaxed structural balance (RSB) approach and its subsequent extension to signed two-mode networks involving social actors and social objects. We extend this approach to large signed two-mode networks, and address the methodological issues that arise. We develop tools to partition these types of networks and compare them with other approaches using a recently collected dataset of United Nations General Assembly roll call votes. Although our primary purpose is methodological, we take the first step towards bridging Heiders structural balance theory with recent theorizing in international relations on soft balancing of power processes.

Analysis of Kinship Relations With Pajek

In the article, two general approaches to analysis of large sparse networks are presented: fragment searching and matrix multiplication. These two approaches are applied to analysis of large genealogies. Genealogies can be represented as graphs in different ways: as Ore graphs, p-graphs, or bipartite p-graphs. We show that p-graphs are more suitable for searching for relinking patterns, whereas Ore graphs are better for computing kinship relations using network multiplication. Algorithms described in this article are implemented in the program Pajek.

Visualisation and analysis of the internet movie database

In this paper, we present a case study for the visualisation and analysis of large and complex temporal multivariate networks derived from the Internet movie database (IMDB). Our approach is to integrate network analysis methods with visualisation in order to address scalability and complexity issues. In particular, we defined new analysis methods such as (p,q)-core and 4-ring to identify important dense subgraphs and short cycles from the huge bipartite graphs. We applied island analysis for a specific time slice in order to identify important and meaningful subgraphs. Further, a temporal Kevin Bacon graph and a temporal two mode network are extracted in order to provide insight and knowledge on the evolution.