Detection of top-k central nodes in social networks: A compressive sensing approach

In analysing the structural organization of a social network, identifying important nodes has been a fundamental problem. The concept of network centrality deals with the assessment of the relative importance of a particular node within the network. Most of the traditional network centrality definitions have a high computational cost and require full knowledge of network topological structure. On the one hand, in many applications we are only interested in detecting the top-k central nodes of the network with the largest values considering a specific centrality metric. On the other hand, it is not feasible to efficiently identify central nodes in a large real-world social network via calculation of centrality values for all nodes. As a result, recent years have witnessed increased attention toward the challenging problem of detecting top k central nodes in social networks with high accuracy and without full knowledge of network topology. To this end, we in this paper present a compressive sensing approach, called CS-TopCent, to efficiently identify such central nodes as a sparsity specification of social networks. Extensive simulation results demonstrate that our method would converge to an accurate solution for a wide range of social networks.