Efficient Maximum Closeness Centrality Group Identification

As a key concept in the social networks, closeness centrality is widely adopted to measure the importance of a node. Many efficient algorithms are developed in the literature to find the top-k closeness centrality nodes. In most of the previous work, nodes are treated as irrelevant individuals for a top-k ranking. However, in many applications, it is required to find a set of nodes that is the most important as a group. In this paper, we extend the concept of closeness centrality to a set of nodes. We aim to find a set of k nodes that has the largest closeness centrality as a whole. We show that the problem is NP-hard, and prove that the objective function is monotonic and submodular. Therefore, the greedy algorithm can return a result with \(1-1/e\) approximation ratio. In order to handle large graphs, we propose a baseline sampling algorithm (BSA). We further improve the sampling approach by considering the order of samples and reducing the marginal gain update cost, which leads to our order based sampling algorithm (OSA). Finally, extensive experiments on four real world social networks demonstrate the efficiency and effectiveness of the proposed methods.