Evolution of Social Power in Networks with Constant Topology

Abstract

This chapter considers the DeGroot–Friedkin model on networks with a constant topology, an assumption which is relaxed in the following chapter. A novel analysis framework is built using nonlinear contraction theory, which allows the drawing of a new and general exponential convergence result. Specifically, it will be shown that each individual’s social power converges exponentially fast to a constant value that depends only on the network topology. Previous results establish asymptotic, but not exponential convergence. Additional analysis yields an explicit upper bound on the individual’s social power at equilibrium that is dependent on the graph topology, and the convergence rates for a general class of graph topologies are obtained.