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A Basis for Systematic Analysis of Network Topologies: Technical Report
P. Mahadevan, D. Krioukov, A. Vahdat, and K. Fall, "A Basis for Systematic Analysis of Network Topologies: Technical Report", Tech. rep., Cooperative Association for Internet Data Analysis (CAIDA), Apr 2006.
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A Basis for Systematic Analysis of Network Topologies: Technical Report

Priya Mahadevan2
Dmitri Krioukov1
Amin Vahdat2
Kevin Fall3

CAIDA, San Diego Supercomputer Center, University of California San Diego


Department of Computer Science and Engineering,
University of California, San Diego


Intel Research, Berkeley

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 graphmetrics 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 (Erdõs-Rényi) 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.

Keywords: topology
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