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This paper analyses the DeGroot-Friedkin model for evolution of theindividuals' social powers in a social network when the network topology variesdynamically (described by dynamic relative interaction matrices). TheDeGroot-Friedkin model describes how individual social power (self-appraisal,self-weight) evolves as a network of individuals discuss a sequence of issues.We seek to study dynamically changing relative interactions becauseinteractions may change depending on the issue being discussed. In order toexplore the problem in detail, two different cases of issue-dependent networktopologies are studied. First, if the topology varies between issues in aperiodic manner, it is shown that the individuals' self-appraisals admit aperiodic solution. Second, if the topology changes arbitrarily, under theassumption that each relative interaction matrix is doubly stochastic andirreducible, the individuals' self-appraisals asymptotically converge to aunique non-trivial equilibrium.

On the Analysis of the DeGroot-Friedkin Model with Dynamic Relative Interaction Matrices