Estimating the number of communities by spectral methods

Community detection is a fundamental problem in network analysis with many methods available to estimate communities. Most of these assume that the number communities known, which often not case practice. We study simple and very fast method for estimating based on spectral properties certain graph operators, such as non-backtracking matrix Bethe Hessian matrix. show performs well under several models wide range parameters, guaranteed be consistent asymptotic regimes. compare this existing it both more accurate computationally efficient.