Opinion Formation over Signed Gossip Networks

Abstract

: Opinion formation is investigated over signed gossip networks, where asymptotic and transient opinion behaviors 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.

Opinion Dynamics via a Gossip Algorithm with Asynchronous Group Interactions

“…Edges may be directed or undirected depending on whether the relationships being represented are asymmetric or not. Since the gossip algorithm considered in [4] applies specifically to symmetric relationships, the scope of the discussion here is restricted to undirected graphs.…”

“…As mentioned in the previous section, the gossip algorithm in [4] is restricted to pairwise interactions. Our work extends the gossip algorithm to allow asynchronous group interactions.…”

“…Our work extends the gossip algorithm to allow asynchronous group interactions. Since this algorithm is an extension of the model described in [4], we also assume that the given graph is undirected and connected.…”

“…As an alternative to the consensus model, opinion propagation can be modeled using probabilistic asynchronous interactions. In [4], a gossip algorithm was used for modeling the opinion dynamics of random pairwise interactions.…”

“…In this paper, we extend the model in [4] by incorporating group interactions. We describe how it is related to the pairwise gossip algorithm and the consensus model, then we compare their behaviors via simulations.…”