A Mathematical Programming approach to Overlapping community detection by cluster's Shapley value

TL;DR

This paper introduces a novel mathematical programming model for detecting overlapping communities in networks using cooperative game theory and mixed-integer linear programming, providing exact solutions for small instances and heuristics for larger ones.

Contribution

It presents a new approach combining cooperative game theory with mixed-integer programming to identify overlapping communities, advancing beyond previous methods.

Findings

Exact solutions for small/medium networks improve understanding of network structure.

Heuristic algorithms enable analysis of larger networks.

Comparison of objective function variations informs method effectiveness.

Abstract

We propose a new model to detect the overlapping communities of a network that is based on cooperative games and mathematical programming. More specifically, communities are defined as stable coalitions of a weighted graph community game and they are revealed as the optimal solution of a mixed-integer linear programming problem. Exact optimal solutions are obtained for small and medium sized instances and and it is shown that they provide useful information about the network structure, improving on previous contributions. Next, a heuristic algorithm is developed to solve the largest instances and used to compare two variations of the objective function.