Signed Quasi-Clique Merger: A New Clustering Method for Signed Networks with Positive and Negative Edges

Signed networks with both positive and negative links have gained considerable attention over the past several years. Community detection is among the main challenges for signed network analysis. It aims to find mutually antagonistic groups such that entities within the same group have as many positive relationships as possible and entities between different groups have as many negative relationships as possible. Most existing algorithms for community detection in signed networks aim to provide a hard partition of the network where any node should belong to a single community. However, overlapping communities, where a node is allowed to belong to multiple communities, widely exist in many real-world networks. Another disadvantage of some existing algorithms is that the number of final clusters k should be an input of the clustering process. It may however be the case that we do not know k in advance. In this paper, to offer improvements to existing algorithms, we propose a new clustering method for signed networks, the Signed Quasi-clique Merger (SQCM) algorithm. This algorithm detects the meaningful clusters (i.e. subgraphs with high friendly density) from the networks directly, where the friendly density of a subgraph C=(V(C),E(C)) is defined as d(C)=2∑e∈E(C)w(e)|V(C)|(|V(C)|−1). We construct a hierarchically nested system to illustrate their inclusion relationships. The output of SQCM is a smaller hierarchical tree, which clearly highlights meaningful clusters. During the clustering process, we do not need to know the number of final clusters k in advance; the algorithm is able to detect it on its own. Another important feature of SQCM is overlapping clustering or multi-membership. Its effectiveness is demonstrated through rigorous experiments involving both benchmark and randomly generated signed networks.