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A Review of and Some Results for Ollivier–Ricci Network Curvature

Author

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  • Nazanin Azarhooshang

    (Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
    These authors contributed equally to this work.)

  • Prithviraj Sengupta

    (Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
    These authors contributed equally to this work.)

  • Bhaskar DasGupta

    (Department of Computer Science, University of Illinois at Chicago, Chicago, IL 60607, USA
    These authors contributed equally to this work.)

Abstract

Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from the non-network domains in a suitable way to the network science domain. In this article we discuss one such extension, namely Ollivier’s discretization of Ricci curvature. We first motivate, define and illustrate the Ollivier–Ricci Curvature. In the next section we provide some “not-previously-published” bounds on the exact and approximate computation of the curvature measure. In the penultimate section we review a method based on the linear sketching technique for efficient approximate computation of the Ollivier–Ricci network curvature. Finally in the last section we provide concluding remarks with pointers for further reading.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1416-:d:403126
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    References listed on IDEAS

    as
    1. 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.
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