Community Detection in Sparse Realistic Graphs: Improving the Bethe Hessian

This article improves over the recently proposed Bethe Hessian matrix for community detection on sparse graphs, assuming here a more realistic setting where node degrees are inhomogeneous. We notably show that the parametrization proposed in the seminal work on the Bethe Hessian clustering can be ameliorated with positive consequences on correct classification rates. Extensive simulations support our claims.