Topological implications of negative curvature for biological and social networks

Réka Albert, Bhaskar DasGupta, and Nasim Mobasheri
Phys. Rev. E 89, 032811 – Published 24 March 2014
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Abstract

Network measures that reflect the most salient properties of complex large-scale networks are in high demand in the network research community. In this paper we adapt a combinatorial measure of negative curvature (also called hyperbolicity) to parametrized finite networks, and show that a variety of biological and social networks are hyperbolic. This hyperbolicity property has strong implications on the higher-order connectivity and other topological properties of these networks. Specifically, we derive and prove bounds on the distance among shortest or approximately shortest paths in hyperbolic networks. We describe two implications of these bounds to crosstalk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.

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  • Received 11 September 2013
  • Revised 16 February 2014

DOI:https://doi.org/10.1103/PhysRevE.89.032811

©2014 American Physical Society

Authors & Affiliations

Réka Albert*

  • Department of Physics, Pennsylvania State University, University Park, Pennsylvania 16802, USA

Bhaskar DasGupta and Nasim Mobasheri

  • Department of Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607, USA

  • *ralbert@phys.psu.edu
  • dasgupta@cs.uic.edu
  • nmobas2@uic.edu

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Issue

Vol. 89, Iss. 3 — March 2014

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