Exponential random graphs as models of overlay networks

TL;DR

This paper provides an analytic solution for exponential random graph models with fixed degree sequences, analyzing their degree distribution, expansion, conductance, and resilience, with applications to overlay networks in P2P systems.

Contribution

It introduces an analytic approach to exponential random graphs with fixed degree sequences and applies it to analyze properties relevant to overlay network design.

Findings

Degrees are concentrated around their mean value.

Derived asymptotic results for graph expansion and conductance.

Analyzed graph resilience to random failures.

Abstract

In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the context of load balancing in communication networks, namely Peer-to-Peer overlays. We then analyse the degree distribution of such graphs and show that the degrees are concentrated around their mean value. Finally, we derive asymptotic results on the number of edges crossing a graph cut and use these results $(i)$ to compute the graph expansion and conductance, and $(ii)$ to analyse the graph resilience to random failures.