Systematic topology analysis and generation using degree correlations

By Priya Mahadevan, Dmitri V. Krioukov, Kevin R. Fall, Amin Vahdat. Conference on Applications, Technologies, Architectures, and Protocols for Computer Communication, 2006

382 citations recorded by the source corpus.

Researchers have proposed a variety of metrics to measure important graph properties, for instance, in social, biological, and computer networks. Values for a particular graph metric may capture a graph's resilience to failure or its routing efficiency. Knowledge of appropriate metric values may influence the engineering of future topologies, repair strategies in the face of failure, and understanding of fundamental properties of existing networks. Unfortunately, there are typically no algorithms to generate graphs matching one or more proposed metrics and there is little understanding of the relationships among individual metrics or their applicability to different settings. 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.

Subfields: Computer Networks and Communications, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3d983dad35f7fd84a2dff7bc47b320f7e73fc9ce

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Citations in the corpus

Accurate Estimation of the Degree Distribution of Private Networks (2009, background): “It influences the structure of a graph and processes that operate on a graph, and a diverse line of research has studied properties of random ensembles of graphs consistent with a known degree distribution [12], [14], [18].”
The statistical physics of real-world networks (2018, background): “aiming at generating ensembles of networks with desired degree distribution, degree-degree correlations and clustering coefficient (within the so-called dk-series approach) [137, 138].”
Can ISPS and P2P users cooperate for improved performance? (2007, methodology): “Hence, we make the basis for our simulations the current AS topology of the Internet [31, 32], as it can be derived from the BGP routing information.”
Networks beyond pairwise interactions: structure and dynamics (2020, methodology): “As an example, generative models aimed to quantify randomness in networks via motif-based constraints [61] were shown to become very hard to manage, or even sample, for interactions above order 2 [62].”