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arXiv · 2306.06474

Augmentations of Forman's Ricci Curvature and their Applications in Community Detection

Lukas Fesser·Sergio Serrano de Haro Iváñez·Karel Devriendt·Melanie Weber·Renaud Lambiotte
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Abstract

The notion of curvature on graphs has recently gained traction in the networks community, with the Ollivier-Ricci curvature (ORC) in particular being used for several tasks in network analysis, such as community detection. In this work, we choose a different approach and study augmentations of the discretization of the Ricci curvature proposed by Forman (AFRC). We empirically and theoretically investigate its relation to the ORC and the un-augmented Forman-Ricci curvature. In particular, we provide evidence that the AFRC frequently gives sufficient insight into the structure of a network to be used for community detection, and therefore provides a computationally cheaper alternative to previous ORC-based methods. Our novel AFRC-based community detection algorithm is competitive with an ORC-based approach.

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Lukas Fesser, Sergio Serrano de Haro Iváñez, Karel Devriendt, Melanie Weber, Renaud Lambiotte. 2023-06-10. Augmentations of Forman's Ricci Curvature and their Applications in Community Detection. https://doi.org/10.1088/2632-072x%2Fad64a3

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