Topological implications of negative curvature for biological and social networks

Réka Albert, Bhaskar DasGupta, Nasim Mobasheri
2014 Physical Review E  
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 parameterized 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,
more » ... 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 cross-talk in biological networks, and to the existence of central, influential neighborhoods in both biological and social networks.
doi:10.1103/physreve.89.032811 pmid:24730903 fatcat:aerrdi32ura5rf7ff4d2etwfwi