Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian

• URL: http://arxiv.org/abs/2006.04510v2
• Date: Mon, 26 Oct 2020 09:17:16 GMT
• Title: Community detection in sparse time-evolving graphs with a dynamical Bethe-Hessian
• Authors: Lorenzo Dall'Amico, Romain Couillet, Nicolas Tremblay
• Abstract summary: 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.
• Score: 47.82639003096941
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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