Stable configurations in social networks. (25th April 2018)

• Record Type: Journal Article
• Authors: Bronski, Jared C; DeVille, Lee; Ferguson, Timothy; Livesay, Michael
• Is Part Of: Nonlinearity. Volume 31:Number 6(2018:Jun.)
• Page Start: 2518
• Page End: 2531
• Publication Date: 2018-04-25
• Subjects: social network -- balanced graph -- graph Laplacian -- Poincare–Miranda theorem -- complex potential -- bifurcation -- opinion formation; 37G05 -- 34C23 -- 34D30; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aab0b5
• Languages: English
• ISSNs: 0951-7715

Abstract

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.