Augmentations of Forman’s Ricci curvature and their applications in community detection

• DOI: 10.1088/2632-072x/ad64a3
• Publication Date: 2024-07-17T22:58:31Z
• Authors: Lukas Fesser; Sergio Serrano de...; Karel Devriendt; Melanie Weber; Renaud Lambiotte
• Keywords: FOS: Computer and information sciences; Discrete Mathematics (cs.DM); Science; Physics; QC1-999; Q; Metric Geometry (math.MG); 05C82, 05C10 (Primary) 53C21, 68R10, 05C75 (Secondary); discrete curvature; Mathematics - Metric Geometry; community detection; FOS: Mathematics; Mathematics - Combinatorics; Combinatorics (math.CO); network analysis; Computer Science - Discrete Mathematics

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