A critical point for random graphs with a given degree sequence
Random Graphs 93 Proceedings of the sixth international seminar on Random graphs and probabilistic methods in combinatorics and computer science
A random graph model for massive graphs
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The Size of the Giant Component of a Random Graph with a Given Degree Sequence
Combinatorics, Probability and Computing
Systematic topology analysis and generation using degree correlations
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
Orbis: rescaling degree correlations to generate annotated internet topologies
Proceedings of the 2007 conference on Applications, technologies, architectures, and protocols for computer communications
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We propose a framework for modeling higher-order (beyond two point) degree correlation among nodes, depending on their mutual connectivity. Our focus is on the introduction of the Markov property to find maximally unbiased networks under the constraint of a prescribed two-point degree correlation. 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 AS- and router-level topologies in terms of whether they are Markovian or not. The results of the analysis show that the studied AS- and router-level topologies are not Markovian. This finding indicates that it is rather difficult to capture the topological characteristics of the Internet either at AS- or at router-level solely by the input of the two-point degree correlation.