Finding Antagonistic Communities in Signed Uncertain Graphs

Many real-world networks are signed networks with positive and negative edge weights, such as social networks with positive (friend) or negative (foe) relationships between users, and gene interaction networks with positive (stimulatory) or negative (inhibitory) interactions between genes. A well-known data mining task in signed networks is to find groups of antagonistic communities, where the vertices in the same community have a strong positive relationship and the vertices in different communities have a strong negative relationship. Most existing methods find antagonistic communities by modelling a signed network as a static graph with constant positive and negative edge weights. However, since the relationship between vertices is often uncertain in many real-world networks, it is more practical and accurate to capture the uncertainty of the relationship in the network by a signed uncertain graph (SUG), where each edge is independently associated with a discrete probability distribution of signed edge weights. How to find groups of antagonistic communities in a SUG is a challenging data mining task that has not been systematically tackled before. In this paper, we propose a novel method to tackle this task. We first model a group of antagonistic communities by a set of subgraphs, where the vertices in the same subgraph have a large expectation of positive edge weights and the vertices in different subgraphs have a large expectation of negative edge weights. Then, we propose a method to efficiently find significant groups of antagonistic communities by restricting all the computations on small local subgraphs of the SUG. Extensive experiments on seven real-world datasets and a synthetic dataset demonstrate the outstanding effectiveness and efficiency of the proposed method.