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Forman-Ricci curvature and persistent homology of unweighted complex networks

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

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.

Suggested Citation

  • Roy, Indrava & Vijayaraghavan, Sudharsan & Ramaia, Sarath Jyotsna & Samal, Areejit, 2020. "Forman-Ricci curvature and persistent homology of unweighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920306561
    DOI: 10.1016/j.chaos.2020.110260
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    References listed on IDEAS

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    1. Giovanni Petri & Martina Scolamiero & Irene Donato & Francesco Vaccarino, 2013. "Topological Strata of Weighted Complex Networks," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-8, June.
    2. Saucan, Emil & Sreejith, R.P. & Vivek-Ananth, R.P. & Jost, Jürgen & Samal, Areejit, 2019. "Discrete Ricci curvatures for directed networks," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 347-360.
    3. L. Šubelj & M. Bajec, 2011. "Robust network community detection using balanced propagation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 81(3), pages 353-362, June.
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