Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian
Abstract
This article considers the problem of community detection in sparse dynamical graphs in which the community structure evolves over time. A fast spectral algorithm based on an extension of the Bethe-Hessian matrix is proposed, which benefits from the positive correlation in the class labels and in their temporal evolution and is designed to be applicable to any dynamical graph with a community structure. Under the dynamical degree-corrected stochastic block model, in the case of two classes of equal size, we demonstrate and support with extensive simulations that our proposed algorithm is capable of making non-trivial community reconstruction as soon as theoretically possible, thereby reaching the optimal detectability threshold and provably outperforming competing spectral methods.
Cite
@article{arxiv.2006.04510,
title = {Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian},
author = {Lorenzo Dall'Amico and Romain Couillet and Nicolas Tremblay},
journal= {arXiv preprint arXiv:2006.04510},
year = {2020}
}