Network partitioning algorithms as cooperative games

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.

Statistical Analysis of Networks

“…Inspired by path-discounting characteristic functions of Jackson and Wolinsky, 1996;Jackson, 2010, in Mazalov andTrukhina, 2014;Mazalov et al, 2016 for trees andin Avrachenkov et al, 2018a for general graphs, the following characteristic function was proposed. Let δ ∈ [0, 1] be a discount factor.…”

“…In Avrachenkov et al, 2018a it was shown that this characteristic function leads to a manageable expression for the Myerson value:…”

Cluster-size constrained network partitioning

“…Finally, the third class of methods to network partitioning is based on the optimization of some objective such as likelihood [8,9], modularity [10] or energy function [11,12]. Interestingly, many mentioned approaches can also be viewed as particular instances of hedonic game [13]. The approach developed in this paper is also based on the energy function optimization.…”

A Cooperative Network Packing Game with Simple Paths

“…Graph clustering problems can be treated as cooperative games with a Nash stable coalition partition when none of the players benefit from changing the coalition structure. In this case, the Myerson value is used as an allocation principle; see [17,18].…”