A Novel Interpretation for Opinion Consensus in Social Networks With Antagonisms

We take a new perspective for the consensus in DeGroot-type social networks with antagonistic interactions between some pairs of agents. We observe the analogies between social networks and electrical networks. A line with positive (or negative) conductance in the electrical network well corresponds to the cooperative (or antagonistic) interaction in the social network. Then, we introduce a refined definition of effective conductance (EC), which comes from electrical networks, into social networks as a characterization of the overall relationship between a pair of agents. The EC considers the effects of both direct and indirect interactions between the agents. Some EC-based consensus criteria are established by analytical and statistical approaches, showing that the sign of EC is a useful indicator of consensus. The opinion consensus can be generally interpreted as every pair of agents being overall cooperative despite antagonistic interactions, i.e., the corresponding EC being positive. The obtained results provide new insights into the consensus mechanism with clear intuition. Case study of a 15-agent network is provided as an illustration.