Social balance-based centrality measure for directed signed networks

We suggest a novel approach to determining the centrality measures for directed signed networks, based on the notion of social balance. We postulate that along with the existing positive connections, the structure of positive and negative connections can be used to determine potential secondary connections, respectively, weak social ties between pairs of individuals who are, e.g., either friends with the same person or under threat from the same person. This kind of connection agrees perfectly with the theory of social balance. Given the structure of primary and secondary connections, the centrality is measured using an eigenvector-based scheme. The suggested approach is applied to the classical example of the social network of monks in a monastery, and the results show a good agreement with the available ground truth.