Clique Relaxations in Social Network Analysis: The Maximum k-Plex Problem

This paper introduces and studies the maximum k-plex problem, which arises in social network analysis and has wider applicability in several important areas employing graph-based data mining. After establishing NP-completeness of the decision version of the problem on arbitrary graphs, an integer programming formulation is presented followed by a polyhedral study to identify combinatorial valid inequalities and facets. A branch-and-cut algorithm is implemented and tested on proposed benchmark instances. An algorithmic approach is developed exploiting the graph-theoretic properties of a k-plex, that is effective in solving the problem to optimality on very large, sparse graphs such as the power law graphs frequently encountered in the applications of interest. Keywords. maximum k-plex problem; maximum clique problem; social network analysis; clique relaxations; cohesive subgroups; scale free graphs; power law graphs

• Type: Journal
• Year: 2011
• Where: IOR
• Authors: Balabhaskar Balasundaram, Sergiy Butenko, Illya V. Hicks
• Keywords: IOR 2011, Maximum K-plex Problem, Power Law, Social Network Analysis