Network partitioning algorithms as cooperative games

Konstantin E Avrachenkov,Vladimir V Mazalov,Aleksei Y Kondratev,Dmytro G Rubanov

doi:10.1186/s40649-018-0059-5

Abstract

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.

Highlights

Community detection in networks is a very important topic which has numerous applications in social network analysis, computer science, telecommunications, and bioinformatics and has attracted the effort of many researchers
We consider the framework of crisp community detection or network partitioning, where one would like to partition a network into disjoint sets of nodes
The first approach is based on the Myerson value for graph constrained cooperative game, whereas the second approach is based on hedonic games which explain coalition formation

Summary

Introduction

Community detection in networks is a very important topic which has numerous applications in social network analysis, computer science, telecommunications, and bioinformatics and has attracted the effort of many researchers. We consider the framework of crisp community detection or network partitioning, where one would like to partition a network into disjoint sets of nodes. The first very large class is based on spectral elements of the network matrices such as adjacency matrix and Laplacian (see e.g., the surveys [1, 5] and references therein). The second class of methods is based on the use of random walks (see e.g., [7,8,9,10,11,12] for the most representative works in this research direction). We recommend to an interested reader a recent survey [4] on the application of game-theoretic techniques

Objectives

Conclusion