Network, Popularity and Social Cohesion: A Game-Theoretic Approach

TL;DR

This paper introduces a game-theoretic model of social cohesion based on network topology and individual social needs, analyzing stability and computational complexity, and proposing heuristics for identifying cohesive groups.

Contribution

It presents a novel cooperative game model linking social cohesion to network structure and stability, and provides computational methods and heuristics for assessing cohesion.

Findings

Social cohesion relates to core stability of grand coalition.

Deciding social cohesion is CoNP-complete.

Heuristics effectively identify high-popularity coalition structures.

Abstract

In studies of social dynamics, cohesion refers to a group's tendency to stay in unity, which -- as argued in sociometry -- arises from the network topology of interpersonal ties between members of the group. We follow this idea and propose a game-based model of cohesion that not only relies on the social network, but also reflects individuals' social needs. In particular, our model is a type of cooperative games where players may gain popularity by strategically forming groups. A group is socially cohesive if the grand coalition is core stable. We study social cohesion in some special types of graphs and draw a link between social cohesion and the classical notion of structural cohesion. We then focus on the problem of deciding whether a given social network is socially cohesive and show that this problem is CoNP-complete. Nevertheless, we give two efficient heuristics for coalition structures where players enjoy high popularity and experimentally evaluate their performances.