Energy Landscape of Social Balance

2009/06/30 by Seth A. Marvel, Steven H. Strogatz, Jon Kleinberg +1
Mathematics · Physics and Astronomy · Psychology · #Balance (ability) #Complex Network Analysis Techniques #Computer science #Detailed balance #Energy (signal processing) #Energy landscape #Mathematical analysis #Mathematics #Maxima and minima #Mental Health Research Topics #Modular design #Opinion Dynamics and Social Influence #Physics #Psychology #Quantum mechanics #Sign (mathematics) #Sociology #Statistical physics #nlin.AO #physics.soc-ph

paper · pdf · doi:10.1103/physrevlett.103.198701

4 pages, 3 figures

arxiv created 2009/08/25 · openalex publication_date 2009/11/04 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Random Graphs
• Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters
• Attitudes and Cognitive Organization
• A ferromagnet with a glass transition
• Random graph gauge theories as toy models for non-perturbative string theories
• Structural balance: a generalization of Heider's theory.
• Evolution of networks
• Dynamics of social balance on networks
• The Structure and Function of Complex Networks
• On Orthogonal Matrices
• The psychology of interpersonal relations.