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Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence

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  • Charo I Del Genio
  • Hyunju Kim
  • Zoltán Toroczkai
  • Kevin E Bassler

Abstract

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large , and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.

Suggested Citation

  • Charo I Del Genio & Hyunju Kim & Zoltán Toroczkai & Kevin E Bassler, 2010. "Efficient and Exact Sampling of Simple Graphs with Given Arbitrary Degree Sequence," PLOS ONE, Public Library of Science, vol. 5(4), pages 1-7, April.
  • Handle: RePEc:plo:pone00:0010012
    DOI: 10.1371/journal.pone.0010012
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    Cited by:

    1. Shaun Lichter & Christopher Griffin & Terry Friesz, 2023. "The Calculation and Simulation of the Price of Anarchy for Network Formation Games," Networks and Spatial Economics, Springer, vol. 23(3), pages 581-610, September.
    2. Bryan S. Graham, 2015. "Methods of Identification in Social Networks," Annual Review of Economics, Annual Reviews, vol. 7(1), pages 465-485, August.
    3. Stephan Bialonski & Martin Wendler & Klaus Lehnertz, 2011. "Unraveling Spurious Properties of Interaction Networks with Tailored Random Networks," PLOS ONE, Public Library of Science, vol. 6(8), pages 1-13, August.
    4. Qing Cai & Mahardhika Pratama & Sameer Alam, 2019. "Interdependency and Vulnerability of Multipartite Networks under Target Node Attacks," Complexity, Hindawi, vol. 2019, pages 1-16, November.
    5. Chorozoglou, D. & Papadimitriou, E. & Kugiumtzis, D., 2019. "Investigating small-world and scale-free structure of earthquake networks in Greece," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 143-152.
    6. Chorozoglou, D. & Kugiumtzis, D. & Papadimitriou, E., 2018. "Testing the structure of earthquake networks from multivariate time series of successive main shocks in Greece," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 28-39.
    7. D. Chorozoglou & E. Papadimitriou, 2020. "Investigation of earthquake recurrence networks: the cases of 2014 and 2015 aftershock sequences in Ionian Islands, Greece," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 102(3), pages 783-805, July.
    8. Andrin Pelican & Bryan S. Graham, 2020. "An Optimal Test for Strategic Interaction in Social and Economic Network Formation between Heterogeneous Agents," NBER Working Papers 27793, National Bureau of Economic Research, Inc.
    9. Zhang, Linjun & Small, Michael & Judd, Kevin, 2015. "Exactly scale-free scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 182-197.

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