Whom to trust in a signed network? Optimal solution and two heuristic rules

Abstract

Signed networks capture both positive and negative relationships in a social network. We assume that the network nodes are of two different types and, in agreement with social balance theory, link signs correlate with node types. Given a signed network and information on the type of some source nodes, we study the problem of judging the type of a target node. We first formulate a globally optimal Bayes solution to this problem. As this optimal solution is too complex to be used by humans, we proceed by introducing a heuristic based on the shortest paths between the source nodes and the target node. We prove that this heuristic is weakly better than a previously introduced heuristic based on random walks, and that it coincides with the optimal rule for star-like networks. With simulations, we assess the accuracy of the three type-judging rules and find that our heuristic is particularly accurate for networks with short distances and when there are multiple source nodes. Our work contributes to the active field of inference in complex networks and puts emphasis on methods that could be applied by humans facing network data.