Stable configurations in social networks

Jared C. Bronski, Lee Deville, Timothy Ferguson, Michael Livesay

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2518-2531
Number of pages14
Issue number6
StatePublished - Apr 25 2018


  • PoincareMiranda theorem
  • balanced graph
  • bifurcation
  • complex potential
  • graph Laplacian
  • opinion formation
  • social network

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics


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