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Type: Journal article
Title: Generating connected random graphs
Author: Gray, C.
Mitchell, L.
Roughan, M.
Citation: Journal of Complex Networks, 2019; 7(6):896-912
Publisher: Oxford University Press (OUP)
Issue Date: 2019
ISSN: 2051-1310
Statement of
Caitlin Gray, Lewis Mitchell and Matthew Roughan
Abstract: Sampling random graphs is essential in many applications, and often algorithms use Markov chain Monte Carlo methods to sample uniformly from the space of graphs. However, often there is a need to sample graphs with some property that we are unable, or it is too inefficient, to sample using standard approaches. In this paper, we are interested in sampling graphs from a conditional ensemble of the underlying graph model. We present an algorithm to generate samples from an ensemble of connected random graphs using a Metropolis-Hastings framework. The algorithm extends to a general framework for sampling from a known distribution of graphs, conditioned on a desired property. We demonstrate the method to generate connected spatially embedded random graphs, specifically the well known Waxman network, and illustrate the convergence and practicalities of the algorithm.
Keywords: random graphs; MCMC; network sampling; connected networks
Description: Advance Access Publication on 20 March 2019
Rights: © The authors 2019. Published by Oxford University Press. All rights reserved.
DOI: 10.1093/comnet/cnz011
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Mathematical Sciences publications

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