Community detection in graphs

TL;DR

This paper provides a comprehensive overview of community detection in graphs, discussing its significance, challenges, various methods including those from statistical physics, and applications to real-world networks.

Contribution

It offers a thorough exposition of community detection techniques, emphasizing methods developed by statistical physicists and addressing key issues like significance testing and method comparison.

Findings

Community detection is crucial for understanding complex systems.

Various methods exist, with a focus on statistical physics approaches.

Applications demonstrate the practical relevance of community detection.

Abstract

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.