A degree-based block model and a local expansion optimization algorithm for anti-community detection in networks

Anti-community detection in networks can discover negative relations among objects. However, a few researches pay attention to detecting anti-community structure and they do not consider the node degree and most of them require high computational cost. Block models are promising methods for exploring modular regularities, but their results are highly dependent on the observed structure. In this paper, we first propose a Degree-based Block Model (DBM) for anti-community structure. DBM takes the node degree into consideration and evolves a new objective function Q(C) for evaluation. And then, a Local Expansion Optimization Algorithm (LEOA), which preferentially considers the nodes with high degree, is proposed for anti-community detection. LEOA consists of three stages: structural center detection, local anti-community expansion and group membership adjustment. Based on the formulation of DBM, we develop a synthetic benchmark DBM-Net for evaluating comparison algorithms in detecting known anti-community structures. Experiments on DBM-Net with up to 100000 nodes and 17 real-world networks demonstrate the effectiveness and efficiency of LEOA for anti-community detection in networks.