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Forman’s Ricci Curvature - From Networks to Hypernetworks

  • Emil Saucan
  • Melanie Weber
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 812)

Abstract

Networks and their higher order generalizations, such as hypernetworks or multiplex networks are ever more popular models in the applied sciences. However, methods developed for the study of their structural properties go little beyond the common name and the heavy reliance of combinatorial tools. We show that, in fact, a geometric unifying approach is possible, by viewing them as polyhedral complexes endowed with a simple, yet, the powerful notion of curvature – the Forman Ricci curvature. We systematically explore some aspects related to the modeling of weighted and directed hypernetworks and present expressive and natural choices involved in their definitions. A benefit of this approach is a simple method of structure-preserving embedding of hypernetworks in Euclidean N-space. Furthermore, we introduce a simple and efficient manner of computing the well established Ollivier-Ricci curvature of a hypernetwork.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ORT Braude CollegeKarmielIsrael
  2. 2.Princeton UniversityPrincetonUSA

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