Centrality measures and opinion dynamics in two-layer networks with replica nodes

We propose two fast and accurate algorithms to approximate game-theoretic centrality measures and examine connection between centrality measures, network properties, and key performance indicators (consensus time and winning rate) of opinion dynamic processes on such networks. As an example, we consider a Zachary’s karate club as a social network and extend it by adding the second (internal) layer of communication. The internal layer represents the network where individuals can share their real opinions with the close friends. The structures of the external and internal layers may be different. The significant positive correlation between internal graph density and consensus time, and significant negative correlation between centrality of authoritative nodes and consensus time are found. The proposed algorithms are verified by a series of experiments from two aspects: the accuracy and the efficiency. The algorithms are novel and can be considered as a contribution to the network theory independently of opinion dynamics as they can be used to calculate node centrality in any weighted graph.