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Jaccard Curvature—an Efficient Proxy for Ollivier-Ricci Curvature in Graphs

  • Siddharth Pal
  • Feng Yu
  • Terrence J. Moore
  • Ram Ramanathan
  • Amotz Bar-Noy
  • Ananthram Swami
Conference paper
Part of the Springer Proceedings in Complexity book series (SPCOM)

Abstract

The discrete version of the Ollivier-Ricci (OR) curvature, applicable to networks, has recently found utility in diverse fields. OR curvature requires solving an optimal mass transport problem for each edge, which can be computationally expensive for large and/or dense networks. We propose two alternative proxies of curvature to OR that are motivated by the Jaccard index and are demonstrably less computationally intensive. Jaccard curvature (JC) is a simple shift and scaling of the Jaccard index that captures the overlap of edge node neighborhoods. Generalized Jaccard curvature (gJC) captures the shortest path distances in a mass exchange problem. We study the goodness of approximation between the proposed curvatures and an alternative metric, Forman-Ricci curvature, with OR curvature for several network models and real networks. Our results suggest that the gJC exhibits a reasonably good fit to the OR curvature for a wide range of networks, while the JC is shown to be a good proxy only for certain scenarios.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Siddharth Pal
    • 1
  • Feng Yu
    • 2
  • Terrence J. Moore
    • 3
  • Ram Ramanathan
    • 4
  • Amotz Bar-Noy
    • 2
  • Ananthram Swami
    • 3
  1. 1.Raytheon BBN TechnologiesCambridgeUSA
  2. 2.City University of New YorkNew York CityUSA
  3. 3.U.S. Army Research LabadelphiUSA
  4. 4.Gotenna IncNew York CityUSA

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