Estimation of Number of Communities in Assortative Sparse Networks
Most community detection algorithms assume the number of communities, K, to be known a priori. Of the various approaches that have been proposed to estimate K, the non-parametric method based on the spectral properties of the Bethe Hessian matrix has garnered much popularity for its simplicity, computational efficiency, and robustness to sparsity of data. Recently, its consistency for networks in semi-dense regimes with the expected degree greater than log(N) has been shown (N being the number of nodes in the network). In this paper, we show that the spectral method based on the Bethe Hessian matrix is in fact also consistent in sparse regimes with expected degree lesser than log(N) at any rate, thus establishing it as a method which is robust to a wide range of problem settings, regardless of the sparsity of networks.
PDF Abstract
