The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

Over the past decade, there has been an explosion of interest in network research across the physical and social sciences. For social scientists, the theory of networks has been a gold mine, yielding explanations for social phenomena in a wide variety of disciplines from psychology to economics. Here, we review the kinds of things that social scientists have tried to explain using social network analysis and provide a nutshell description of the basic assumptions, goals, and explanatory mechanisms prevalent in the field. We hope to contribute to a dialogue among researchers from across the physical and social sciences who share a common interest in understanding the antecedents and consequences of network phenomena.

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Network Analysis in the Social Sciences

The structure and dynamics of multilayer networks

This paper presents a dynamic, firm-level study of the role of network resources in determining alliance formation. Such resources inhere not so much within the firm but reside in the interfirm networks in which firms are placed. Data from extensive fieldwork show that by influencing the extent to which firms have access to information about potential partners, such resources are an important catalyst for new alliances, especially because alliances entail considerable hazards. This study also assesses the importance of firms’ capabilities with alliance formation and material resources as determinants of their alliance decisions. I test this dynamic framework and its hypotheses about the role of time-varying network resources and firm capabilities with comprehensive longitudinal multi-industry data on the formation of strategic alliances by a panel of firms between 1970 and 1989. The results confirm field observations that accumulated network resources arising from firm participation in the network of accumulated prior alliances are influential in firms’ decisions to enter into new alliances. This study highlights the importance of network resources that firms derive from their embeddedness in networks for explaining their strategic behavior. Copyright © 1999 John Wiley & Sons, Ltd.

Network location and learning: the influence of network resources and firm capabilities on alliance formation

Matrix methods may be applied to the analysis of experimental data concerning group structure when these data indicate relationships which can be depicted by line diagrams such as sociograms. One may introduce two concepts,n-chain and clique, which have simple relationships to the powers of certain matrices. Using them it is possible to determine the group structure by methods which are both faster and more certain than less systematic methods. This paper describes such a matrix method and applies it to the analysis of practical examples. At several points some unsolved problems in this field are indicated.

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Papers

A method of matrix analysis of group structure.