The energy landscape of social balance

TL;DR

This paper models social networks with positive and negative relationships as an energy landscape, revealing complex structures with many local minima and providing bounds and classifications for these stable configurations.

Contribution

It introduces a rigorous framework for analyzing social balance as an energy landscape, including bounds and modular classification of local minima.

Findings

The energy landscape is complex with many local minima.

Local minima have a modular structure.

Bounds on the energies of local minima are derived.

Abstract

We model a close-knit community of friends and enemies as a fully connected network with positive and negative signs on its edges. Theories from social psychology suggest that certain sign patterns are more stable than others. This notion of social "balance" allows us to define an energy landscape for such networks. Its structure is complex: numerical experiments reveal a landscape dimpled with local minima of widely varying energy levels. We derive rigorous bounds on the energies of these local minima and prove that they have a modular structure that can be used to classify them.