2024/06/18 by Sathyanarayanan Rengaswami, Rengaswami, Sathyanarayanan, Theodora Bourni +3
Computer Science · Mathematics · Medicine · #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Medical Imaging Techniques and Applications #Social and Information Networks (cs.SI) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2407.06197
openalex publication_date 2024/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The connection between curvature and topology is a very well-studied theme in the subject of differential geometry. By suitably defining curvature on networks, the study of this theme has been extended into the domain of network analysis as well. In particular, this has led to curvature-based community detection algorithms. In this paper, we reveal the relation between community structure of a network and the curvature of its edges. In particular, we give apriori bounds on the curvature of intercommunity edges of a graph.