Consensus in social networks with heterogeneous agents and two centers of influence

We consider a model of the opinion dynamics in a social network containing two centers of influence. Network agents can influence the opinions of each other. Opinion dynamics is described by a homogeneous Markov chain. We study the problem of the reachability of a consensus in the network. We examine the network with a special structure, i.e., the set of agents who are not the centers of influence is divided into three subsets: (i) agents whose opinions are influenced by the first center, (ii) agents whose opinions are influenced by both centers, and (iii) agents whose opinions are influenced by the second center. We prove that the consensus in the network is reached. We examine the reachability of the consensus for special social networks. Theoretical results are illustrated by numerical example.