Efficient Signed Clique Search in Signed Networks

Mining cohesive subgraphs from a network is a fundamental problem in network analysis. Most existing cohesive subgraph models are mainly tailored to unsigned networks. In this paper, we study the problem of seeking cohesive subgraphs in a signed network, in which each edge can be positive or negative, denoting friendship or conflict respectively. We propose a novel model, called maximal (alpha, kappa)-clique, that represents a cohesive subgraph in signed networks. Specifically, a maximal (alpha, kappa)-clique is a clique in which every node has at most.. negative neighbors and at least [alpha kappa] positive neighbors (alpha >= 1). We show that the problem of enumerating all maximal (alpha, kappa)cliques in a signed network is NP-hard. To enumerate all maximal (alpha, kappa)-cliques efficiently, we first develop an elegant signed network reduction technique to significantly prune the signed network. Then, we present an efficient branch and bound enumeration algorithm with several carefully-designed pruning rules to enumerate all maximal (alpha, kappa)-cliques in the reduced signed network. The results of extensive experiments on five large real-life datasets demonstrate the efficiency, scalability, and effectiveness of our algorithms.