Random graph models of communication network topologies

TL;DR

This paper analyzes finite-sized power-law random graph models, introducing 'communication range random graphs' to better represent real communication networks like the Internet, and provides analytical insights into their structure.

Contribution

It introduces the concept of 'communication range random graphs' and offers analytical methods to understand finite-sized power-law network structures.

Findings

Finite-sized power-law graphs resemble Internet topology.

New model captures realistic communication constraints.

Analytical bounds shed light on network structure.

Abstract

We consider a variant of so called power-law random graph. A sequence of expected degrees corresponds to a power-law degree distribution with finite mean and infinite variance. In previous works the asymptotic picture with number of nodes limiting to infinity has been considered. It was found that an interesting structure appears. It has resemblance with such graphs like the Internet graph. Some simulations have shown that a finite sized variant has similar properties as well. Here we investigate this case in more analytical fashion, and, with help of some simple lower bounds for large valued expectations of relevant random variables, we can shed some light into this issue. A new term, 'communication range random graph' is introduced to emphasize that some further restrictions are needed to have a relevant random graph model for a reasonable sized communication network, like the Internet. In this case a pleasant model is obtained, giving the opportunity to understand such networks on an intuitive level. This would be beneficial in order to understand, say, how a particular routing works in such networks.