Markov property of correlated random networks and its application to the analysis of the Internet topologies

Abstract

We propose the notion of a Markov property for finding maximally unbiased networks under the constraint of a prescribed two-point degree correlation. We present a framework for modeling the three-point degree correlation - the degree correlation of a subgraph composed of three nodes - on which the Markov property is introduced. The topological features of the Markovian networks - networks satisfying the Markov property - are fully characterized solely by the two-point degree correlation. We theoretically investigate the topological characteristics of Markovian networks and derive the analytical formulas for their graph theoretical metrics. We present a comparative analysis of autonomous-system- (AS-) and router-level topologies in terms of whether they are Markovian. The results of the analysis show that AS-level topologies are Markovian while the router-level topologies are not. The router-level topologies should largely depend on the physical locations of routers, the dependency of which prevents the router-level topologies from being Markovian.