A Basis for Systematic Analysis of Network Topologies

Preprint
Publisher Website
Google Scholar
Abstract
This paper presents a new, systematic approach to analyzing network topologies. We first introduce a series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Using this series, we can quantitatively evaluate how close synthetic topologies are to G, construct graphs that accurately reproduce the values of commonly-used graph metrics of G, and provide a rigorous basis for capturing any future metrics that may be of interest. The d=0 and d=1 cases reduce to the known classical (Erdos-Renyi) random graphs and random graphs with prescribed degree distributions respectively. However, recent research shows that simply reproducing a graph's degree distribution is insufficient for capturing important properties of network topologies. Using our approach, we construct graphs for d=0,1,2,3 and demonstrate that these graphs reproduce, with increasing accuracy, important properties of measured and modeled Internet topologies. We find that the d=2 case is sufficient for most practical purposes, while d=3 essentially reconstructs the Internet AS- and router-level topologies exactly. Overall, the availability of a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.

This publication has 0 references indexed in Scilit: