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

TL;DR

This paper investigates how traffic in hyperbolic networks concentrates on a small set of nodes called the core, providing formal definitions and analyzing properties across different graph types.

Contribution

It introduces a formal definition of the core in hyperbolic graphs and studies its properties, highlighting traffic concentration phenomena.

Findings

Traffic tends to pass through a finite set of nodes in hyperbolic graphs

The core nodes are highly congested and form a central part of the network

Properties of the core are characterized for various graph models

Abstract

In this work we study the asymptotic traffic flow in Gromov's hyperbolic graphs. We prove that under certain mild hypotheses the traffic flow in a hyperbolic graph tends to pass through a finite set of highly congested nodes. These nodes are called the "core" of the graph. We provide a formal definition of the core in a very general context and we study the properties of this set for several graphs.