Systematic Topology Analysis and Generation Using Degree Correlations

TL;DR

This paper introduces a systematic method using the dK-series to analyze and generate network topologies, accurately capturing properties of Internet topologies with increasing d values, especially d=2 and d=3.

Contribution

It develops a new framework for topology analysis and synthesis based on degree correlations, capable of reproducing complex network metrics and topologies.

Findings

d=2 captures most practical properties of Internet topologies

d=3 can exactly reconstruct Internet AS- and router-level topologies

The approach provides a unified way to compare and generate realistic network models

Abstract

We present a new, systematic approach for analyzing network topologies. We first introduce the dK-series of probability distributions specifying all degree correlations within d-sized subgraphs of a given graph G. Increasing values of d capture progressively more properties of G at the cost of more complex representation of the probability distribution. Using this series, we can quantitatively measure the distance between two graphs and construct random graphs that accurately reproduce virtually all metrics proposed in the literature. The nature of the dK-series implies that it will also capture any future metrics that may be proposed. 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. We hope that a systematic method to analyze and synthesize topologies offers a significant improvement to the set of tools available to network topology and protocol researchers.