Non-hyperbolicity in random regular graphs and their traffic characteristics

Abstract

In this paper we prove that random d-regular graphs with d ≥ 3 have traffic congestion of the order O(n log d-13 n) where n is the number of nodes and geodesic routing is used. We also show that these graphs are not asymptotically δ-hyperbolic for any non-negative δ almost surely as n → ∞. © 2013 Versita Warsaw and Springer-Verlag Wien.