Estimating the number of communities in networks by spectral methods
This addresses a practical limitation in network analysis for researchers and practitioners, offering an incremental improvement over prior methods.
The paper tackles the problem of estimating the number of communities in networks, where most methods assume this number is known, by proposing a fast spectral method based on graph operators like the non-backtracking and Bethe Hessian matrices, showing it is more accurate and computationally efficient than existing methods.
Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these methods assume that the number of communities is known, which is often not the case in practice. We study a simple and very fast method for estimating the number of communities based on the spectral properties of certain graph operators, such as the non-backtracking matrix and the Bethe Hessian matrix. We show that the method performs well under several models and a wide range of parameters, and is guaranteed to be consistent under several asymptotic regimes. We compare this method to several existing methods for estimating the number of communities and show that it is both more accurate and more computationally efficient.