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Unformatted text preview: arXiv:0712.2716v1 [physics.soc-ph] 17 Dec 2007 Community Structure in Graphs Santo Fortunato a , Claudio Castellano b a Complex Networks Lagrange Laboratory (CNLL), ISI Foundation, Torino, Italy b SMC, INFM-CNR and Dipartimento di Fisica, Sapienza Uni- versit`a di Roma, P. le A. Moro 2, 00185 Roma, Italy Abstract Graph vertices are often organized into groups that seem to live fairly in- dependently of the rest of the graph, with which they share but a few edges, whereas the relationships between group members are stronger, as shown by the large number of mutual connections. Such groups of vertices, or commu- nities, can be considered as independent compartments of a graph. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. The task is very hard, though, both conceptually, due to the ambiguity in the definition of com- munity and in the discrimination of different partitions and practically, because algorithms must find good partitions among an exponentially large number of them. Other complications are represented by the possible occurrence of hierar- chies, i.e. communities which are nested inside larger communities, and by the existence of overlaps between communities, due to the presence of nodes belong- ing to more groups. All these aspects are dealt with in some detail and many methods are described, from traditional approaches used in computer science and sociology to recent techniques developed mostly within statistical physics. 1 Introduction The origin of graph theory dates back to Eulers solution  of the puzzle of K onigsbergs bridges in 1736. Since then a lot has been learned about graphs and their mathematical properties . In the 20th century they have also become extremely useful as representation of a wide variety of systems in different areas. Biological, social, technological, and information networks can be studied as graphs, and graph analysis has become crucial to understand the features of these systems. For instance, social network analysis started in the 1930s and has become one of the most important topics in sociology [3, 4]. In recent times, the computer revolution has provided scholars with a huge amount of data and computational resources to process and analyse these data. The size of real networks one can potentially handle has also grown considerably, reaching 1 Figure 1: A simple graph with three communities, highlighted by the dashed circles. millions or even billions of vertices. The need to deal with such a large number of units has produced a deep change in the way graphs are approached -....
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This note was uploaded on 05/20/2011 for the course CAP 5515 taught by Professor Ungor during the Spring '08 term at University of Florida.
- Spring '08
- The Land