Sampling strategies for conditional inference on multigraphs

Robert D. Eisinger, Yuguo Chen

Research output: Contribution to journalArticlepeer-review


We propose two new methods for sampling undirected, loopless multigraphs with fixed degree. The first is a sequential importance sampling method, with the proposal based on an asymptotic approximation to the total number of multigraphs with fixed degree. The multigraphs and their associated importance weights can be used to approximate the null distribution of test statistics and additionally estimate the total number of multigraphs. The second is a Markov chain Monte Carlo method that samples multigraphs based on similar moves used to sample contingency tables with fixed margins.We apply both methods to a number of examples and demonstrate excellent performance.

Original languageEnglish (US)
Pages (from-to)649-656
Number of pages8
JournalStatistics and its Interface
Issue number4
StatePublished - 2018


  • Counting problem
  • Exact test
  • Monte Carlo method
  • Multigraph
  • Sequential importance sampling
  • Symmetric contingency table

ASJC Scopus subject areas

  • Statistics and Probability
  • Applied Mathematics


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