Finding a Maximum Clique in Dense Graphs via χ2 Statistics

The maximum clique extraction problem finds extensive application in diverse domains like community discovery in social networks, brain connectivity networks, motif discovery, gene expression in bioinformatics, anomaly detection, road networks and expert graphs. Since the problem is NP-hard, known algorithms for finding a maximum clique can be expensive for large real-life graphs. Current heuristics also fail to provide high accuracy and run-time efficiency for dense networks, quite common in the above domains. In this paper, we propose the ALTHEA heuristic to efficiently extract a maximum clique from a dense graph. We show that ALTHEA, based on chi-square statistical significance, is able to dramatically prune the search space for finding a maximum clique, thereby providing run-time efficiency. Further, experimental results on both real and synthetic graph datasets demonstrate that ALTHEA is highly accurate and robust in detecting a maximum clique.