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Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs

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  • Péter L Erdős
  • Tamás Róbert Mezei
  • István Miklós
  • Dániel Soltész

Abstract

Since 1997 a considerable effort has been spent on the study of the swap (switch) Markov chains on graphic degree sequences. All of these results assume some kind of regularity in the corresponding degree sequences. Recently, Greenhill and Sfragara published a breakthrough paper about irregular normal and directed degree sequences for which rapid mixing of the swap Markov chain is proved. In this paper we present two groups of results. An example from the first group is the following theorem: let d → be a directed degree sequence on n vertices. Denote by Δ the maximum value among all in- and out-degrees and denote by | E → | the number of edges in the realization. Assume furthermore that Δ

Suggested Citation

  • Péter L Erdős & Tamás Róbert Mezei & István Miklós & Dániel Soltész, 2018. "Efficiently sampling the realizations of bounded, irregular degree sequences of bipartite and directed graphs," PLOS ONE, Public Library of Science, vol. 13(8), pages 1-20, August.
    • Handle: RePEc:plo:pone00:0201995
    DOI: 10.1371/journal.pone.0201995
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    Cited by:

    1. Amanatidis, Georgios & Kleer, Pieter, 2022. "Rapid mixing of the switch Markov chain for 2-class joint degree matrices," Other publications TiSEM 8c1a53f0-48a5-4063-a66a-5, Tilburg University, School of Economics and Management.

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