Switch chain mixing times through triangle counts

T. Bannink, R.W. van der Hofstad, C. Stegehuis

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Abstract

Sampling uniform simple graphs with power-law degree distributions with degree exponent τ∈(2,3) is a non-trivial problem. We propose a method to sample uniform simple graphs that uses a constrained version of the configuration model together with a Markov Chain switching method. We test the convergence of this algorithm numerically in the context of the presence of small subgraphs. We then compare the number of triangles in uniform random graphs with the number of triangles in the erased configuration model. Using simulations and heuristic arguments, we conjecture that the number of triangles in the erased configuration model is larger than the number of triangles in the uniform random graph, provided that the graph is sufficiently large.
Original languageEnglish
Article number1711.06137
Number of pages9
JournalarXiv
Issue number1711.06137
Publication statusPublished - 16 Nov 2017

Bibliographical note

7 pages, 8 figures in the main article. 2 pages, 2 figures in the supplementary material

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