  This paper analyses the DeGroot-Friedkin model for evolution of the
individuals' social powers in a social network when the network topology varies
dynamically (described by dynamic relative interaction matrices). The
DeGroot-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 because
interactions may change depending on the issue being discussed. In order to
explore the problem in detail, two different cases of issue-dependent network
topologies are studied. First, if the topology varies between issues in a
periodic manner, it is shown that the individuals' self-appraisals admit a
periodic solution. Second, if the topology changes arbitrarily, under the
assumption that each relative interaction matrix is doubly stochastic and
irreducible, the individuals' self-appraisals asymptotically converge to a
unique non-trivial equilibrium.
