Overlapping Community Detection Optimization and Nash Equilibrium

TL;DR

This paper introduces a novel algorithm for community detection in social networks that optimizes modularity and guarantees a Nash Equilibrium, enabling both partitioning and overlapping community detection.

Contribution

The paper presents a new optimization algorithm with a potential function that ensures reaching a Nash Equilibrium in community detection, accommodating overlapping communities.

Findings

Effective on real-world medium and large datasets

Guarantees convergence to Nash Equilibrium

Supports both partitioning and overlapping community detection

Abstract

Community detection using both graphs and social networks is the focus of many algorithms. Recent methods aimed at optimizing the so-called modularity function proceed by maximizing relations within communities while minimizing inter-community relations. However, given the NP-completeness of the problem, these algorithms are heuristics that do not guarantee an optimum. In this paper, we introduce a new algorithm along with a function that takes an approximate solution and modifies it in order to reach an optimum. This reassignment function is considered a 'potential function' and becomes a necessary condition to asserting that the computed optimum is indeed a Nash Equilibrium. We also use this function to simultaneously show partitioning and overlapping communities, two detection and visualization modes of great value in revealing interesting features of a social network. Our approach is successfully illustrated through several experiments on either real unipartite, multipartite or directed graphs of medium and large-sized datasets.