Asymptotic Traffic Flow in an Hyperbolic Network I: Definition and Properties of the Core

In this work we study the asymptotic traffic behaviour for Gromov's hyperbolic networks as the size of the network increases. We prove that under certain mild hypothesis the traffic in a large hyperbolic network tends to pass through a finite set of highly congested nodes. These nodes will be called the "core" of the network. We provide a formal definition of the core in a very general context and we study the properties of this set for hyperbolic graphs.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Yuliy Baryshnikov, Gabriel H. Tucci
• Keywords: Asymptotic Traffic Behaviour, CORR 2010, Education, Hyperbolic Network, Large Hyperbolic Network