Abstract-A deep community in a graph is a connected component that can only be seen after removal of nodes or edges from the rest of the graph. This paper addresses the problem of detecting deep communities using a new centrality measure, called the local Fiedler vector centrality (LFVC). The LFVC is associated with the sensitivity of algebraic connectivity to node or edge removals. We prove that a greedy node/edge removal strategy, based on successive minimization of LFVC, is nearly as good as the optimal, but intractable, combinatorial batch removal strategy. Under a stochastic block model framework, we show that the greedy LFVC strategy can extract deep communities with probability one as the number of observations becomes large. We apply the greedy LFVC strategy to real-world social network datasets. Compared with conventional community detection methods we demonstrate improved ability to identify important communities and key members in the network.
Chen et al. REF remove nodes or edges based on the local Fiedler vector centrality (LFVC) which is associated with the sensitivity of algebraic connectivity to node or edge removals.
Deep Community Detection
ArXiv
ArXiv
Mathematics Computer Science Physics