Random multigraphs and aggregated triads with fixed degrees

Ove Frank, Termeh Shafie

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Random multigraphs with fixed degrees are obtained by the configuration model or by so called random stub matching. New combinatorial results are given for the global probability distribution of edge multiplicities and its marginal local distributions of loops and edges. The number of multigraphs on triads is determined for arbitrary degrees, and aggregated triads are shown to be useful for analyzing regular and almost regular multigraphs. Relationships between entropy and complexity are given and numerically illustrated for multigraphs with different number of vertices and specified average and variance for the degrees.
Original languageEnglish
Pages (from-to)232-250
Number of pages19
JournalNetwork Science
Issue number2
Early online date28 Dec 2017
Publication statusPublished - 1 Jun 2018


  • aggregated triad
  • complexity and simplicity
  • configuration model
  • edge multiplicity
  • entropy
  • fixed degrees
  • multigraph
  • random stub matching


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