Local Fiedler vector centrality for detection of deep and overlapping communities in networks

In this paper, a new centrality called local Fiedler vector centrality (LFVC) is proposed to analyze the connectivity structure of a graph. It is associated with the sensitivity of algebraic connectivity to node or edge removals and features distributed computations via the associated graph Laplacian matrix. We prove that LFVC can be related to a monotonic submodular set function that guarantees that greedy node or edge removals come within a factor 1-1/e of the optimal non-greedy batch removal strategy. Due to the close relationship between graph topology and community structure, we use LFVC to detect deep and overlapping communities on real-world social network datasets. The results offer new insights on community detection by discovering new significant communities and key members in the network. Notably, LFVC is also shown to significantly outperform other well-known centralities for community detection.