Evolution of Social Power in Social Networks with Dynamic Topology

Abstract

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 each individual exponentially forgets its initial social power. Specifically, individual social power is dependent only on the dynamic network topology, and initial (or perceived) social power is forgotten as a result of sequential opinion discussion. Last, 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.

Extended version of submitted journal paper. Includes additional simulation details

References in corpus (4)

• Evolution of Social Power in Social Networks with Dynamic Topology
• On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices
• Nonlinear Mapping Convergence and Application to Social Networks
• Modification of Social Dominance in Social Networks by Selective Adjustment of Interpersonal Weights

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• Social power evolution in influence networks with stubborn individuals
• Analysis of a Nonlinear Opinion Dynamics Model with Biased Assimilation