Forman-Ricci curvature and persistent homology of unweighted complex networks

Indrava Roy, Sudharsan Vijayaraghavan, Sarath Jyotsna Ramaia and Areejit Samal

Chaos, Solitons & Fractals, 2020, vol. 140, issue C

Abstract: We present the application of topological data analysis (TDA) to study unweighted complex networks via their persistent homology. By endowing appropriate weights that capture the inherent topological characteristics of such a network, we convert an unweighted network into a weighted one. Standard TDA tools are then used to compute their persistent homology. To this end, we use two main quantifiers: a local measure based on Forman’s discretized version of Ricci curvature, and a global measure based on edge betweenness centrality. We have employed these methods to study various model and real-world networks. Our results show that persistent homology can be used to distinguish between model and real networks with different topological properties.

Keywords: Complex networks; Persistent homology; Forman-Ricci curvature; Edge betweenness centrality (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306561

DOI: 10.1016/j.chaos.2020.110260

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