Centrality measures and opinion dynamics in two-layer networks with replica nodes
Chi Zhao, Elena Parilina
TL;DR
This work analyzes centrality in two-layer networks with replica nodes and investigates how network structure influences opinion dynamics. It introduces a two-layer-to-one-layer transformation and develops two fast algorithms to approximate game-theoretic centralities based on the Shapley and Myerson values, enabling scalable analysis. Through experiments on Zachary's karate club and synthetic networks, the authors demonstrate a strong positive correlation between internal layer density and consensus time $T_{cons}$, and a strong negative correlation between centrality of authoritative nodes and $T_{cons}$, while showing that the approximations accurately identify key influencers. The methods offer a scalable approach to link multilayer network structure with diffusion-like processes, with potential applications in targeted information spreading and control of opinion dynamics.
Abstract
We examine two-layer networks and centrality measures defined on them. We propose two fast and accurate algorithms to approximate the game-theoretic centrality measures and examine connection between centrality measures and characteristics of opinion dynamic processes on such networks. As an example, we consider a Zachary's karate club social network and extend it by adding the second (internal) layer of communication. Internal layer represents the idea that individuals can share their real opinions with their close friends. The structures of the external and internal layers may be different. As characteristics of opinion dynamic processes we mean consensus time and winning rate of a particular opinion. We find significantly strong positive correlation between internal graph density and consensus time, and significantly strong negative correlation between centrality of authoritative nodes and consensus time.