Evolution of Social Power in Social Networks with Dynamic Topology

Mengbin Ye, Ji Liu, Brian D.O. Anderson, Changbin Yu, Tamer Başar

Research output: Contribution to journalArticlepeer-review


The recently proposed DeGroot-Friedkin model describes the dynamical evolution of individual social power in a social network that holds opinion discussions on a sequence of different issues. This paper revisits that model, and uses nonlinear contraction analysis, among other tools, to establish several novel results. First, we show that for a social network with constant topology, each individual's social power converges to its equilibrium value exponentially fast, whereas previous results only concluded asymptotic convergence. Second, when the network topology is dynamic (i.e., the relative interaction matrix may change between any two successive issues), we show that the initial (perceived) social power of each individual is exponentially forgotten. Specifically, individual social power is dependent only on the dynamic network topology, and initial social power is forgotten as a result of sequential opinion discussion. Finally, we provide an explicit upper bound on an individual's social power as the number of issues discussed tends to infinity; this bound depends only on the network topology. Simulations are provided to illustrate our results.

Original languageEnglish (US)
Article number8289383
Pages (from-to)3793-3808
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number11
StatePublished - Nov 2018
Externally publishedYes


  • Discrete-time
  • dynamic topology
  • nonlinear contraction analysis
  • opinion dynamics
  • social networks
  • social power

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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