Opinion Formation over Signed Gossip Networks

Abstract

Opinion formation is investigated over signed gossip networks, where asymptotic and transient opinion be-haviors are analyzed in detail. The network is modeled by a connected signed graph, where each edge of the graph has positive or negative weight, i.e., these edges represent friendly or hostile relationship. Interactions each of which occurs between two persons chosen randomly follow an asynchronous procedure. Then it is shown that their opinions always converge in mean square and converge almost surely. A convergence time is defined as the smallest time such that it takes for the values of nodes to get within a given neighborhood of the consensus value with high probability, regardless of initial state. An upper bound and a lower bound of the convergence time of the gossip algorithm are given in terms of a structure of the given network.