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.
Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-09-2-0053 (the ARL Network Science CTA). The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation here on. This document does not contain technology or technical data controlled under either the U.S. International Traffic in Arms Regulations or the U.S. Export Administration Regulations.
Ram Ramanathan work done while the author was with Raytheon BBN Technologies.
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Pal, S., Yu, F., Moore, T.J., Ramanathan, R., Bar-Noy, A., Swami, A. (2018). Jaccard Curvature—an Efficient Proxy for Ollivier-Ricci Curvature in Graphs. In: Cornelius, S., Coronges, K., Gonçalves, B., Sinatra, R., Vespignani, A. (eds) Complex Networks IX. CompleNet 2018. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-73198-8_5
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