Influence Clubs in Social Networks

A new model "influence club" for cohesion group in a social network is proposed. It generalizes the definition of k-club and has two advantages. First, the influence between two nodes does not only depend on the their distance but also on the numbers of pathways of different lengths. Second, the new model is more flexible than k-club and can provide middle results between k-club and (k + 1)-club. We propose a branch-and-bound algorithm for finding the maximum influence club. For an n-node graph, the worst-case time complexity is o(n(3)1.6(n)), and it is much more efficient in practical: a graph of 200 nodes can be processed within 2 minutes. The performance compared to k-clubs are tested on random graphs and real data. The experimental results also show the advantages of the influence clubs.