Stable Configurations in Social Networks

TL;DR

This paper introduces a model of opinion formation on social networks using an energy-based approach, analyzing stable configurations and revealing non-monotonic effects of connection strength on their number.

Contribution

It provides a novel analysis of stable opinion configurations in social networks, including conditions for global minimizers and the surprising non-monotonic relationship with connection strength.

Findings

Number of stable configurations can increase with stronger connections.

Global minimizers depend on the structure of the friendship graph.

Model reveals complex effects of social ties on opinion stability.

Abstract

We present and analyze a model of opinion formation on an arbitrary network whose dynamics comes from a global energy function. We study the global and local minimizers of this energy, which we call stable opinion configurations, and describe the global minimizers under certain assumptions on the friendship graph. We show a surprising result that the number of stable configurations is not necessarily monotone in the strength of connection in the social network, i.e. the model sometimes supports more stable configurations when the interpersonal connections are made stronger.