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Systematic evaluation of a new combinatorial curvature for complex networks

Author

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  • Sreejith, R.P.
  • Jost, Jürgen
  • Saucan, Emil
  • Samal, Areejit

Abstract

We have recently introduced Forman’s discretization of Ricci curvature to the realm of complex networks. Forman curvature is an edge-based measure whose mathematical definition elegantly encapsulates the weights of nodes and edges in a complex network. In this contribution, we perform a comparative analysis of Forman curvature with other edge-based measures such as edge betweenness, embeddedness and dispersion in diverse model and real networks. We find that Forman curvature in comparison to embeddedness or dispersion is a better indicator of the importance of an edge for the large-scale connectivity of complex networks. Based on the definition of the Forman curvature of edges, there are two natural ways to define the Forman curvature of nodes in a network. In this contribution, we also examine these two possible definitions of Forman curvature of nodes in diverse model and real networks. Based on our empirical analysis, we find that in practice the unnormalized definition of the Forman curvature of nodes with the choice of combinatorial node weights is a better indicator of the importance of nodes in complex networks.

Suggested Citation

  • Sreejith, R.P. & Jost, Jürgen & Saucan, Emil & Samal, Areejit, 2017. "Systematic evaluation of a new combinatorial curvature for complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 50-67.
    • Handle: RePEc:eee:chsofr:v:101:y:2017:i:c:p:50-67
    DOI: 10.1016/j.chaos.2017.05.021
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    References listed on IDEAS

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    1. Mehatari, Ranjit & Banerjee, Anirban, 2015. "Effect on normalized graph Laplacian spectrum by motif attachment and duplication," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 382-387.
    2. Pablo M. Gleiser & Leon Danon, 2003. "Community Structure In Jazz," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 565-573.
    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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    Cited by:

    1. Nazanin Azarhooshang & Prithviraj Sengupta & Bhaskar DasGupta, 2020. "A Review of and Some Results for Ollivier–Ricci Network Curvature," Mathematics, MDPI, vol. 8(9), pages 1-11, August.
    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. Xinyu Wang & Liang Zhao & Ning Zhang & Liu Feng & Haibo Lin, 2022. "Stability of China's Stock Market: Measure and Forecast by Ricci Curvature on Network," Papers 2204.06692, arXiv.org.

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