Community Structure in Graphs

TL;DR

This paper reviews the concept of community detection in graphs, discussing its importance across disciplines, the challenges involved, and various methods including traditional, statistical physics-based, and hierarchical approaches.

Contribution

It provides a comprehensive overview of community detection, addressing conceptual ambiguities, methodological challenges, and recent advances in the field.

Findings

Multiple methods for community detection are described.

Hierarchies and overlaps in communities are analyzed.

The importance of community detection across disciplines is emphasized.

Abstract

Graph vertices are often organized into groups that seem to live fairly independently 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 communities, 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 community 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 hierarchies, i.e. communities which are nested inside larger communities, and by the existence of overlaps between communities, due to the presence of nodes belonging 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.