Moseman, E.
(2016),
Improving the Computational Efficiency of the Blitzstein–Diaconis Algorithm for Generating Random Graphs of Prescribed Degree, NIST Interagency/Internal Report (NISTIR), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/NIST.IR.8066
(Accessed October 27, 2025)
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Improving the Computational Efficiency of the BlitzsteinDiaconis Algorithm for Generating Random Graphs of Prescribed Degree
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Abstract
When generating a random graph, if more structure is desired than is given in the popular Erd\H{o}s Renyi model, one method is to generate a degree sequence first then create a graph with this degree sequence. Blitzstein and Diaconis (among others) developed a sequential algorithm to create a random graph from a degree sequence. This algorithm is assured to always terminate in a graph with the degree sequence; unfortunately, it is slow. This work focuses on the subroutine of the previous algorithm which determines the candidate edges, improving the runtime of the overall algorithm from O(mn2) to O(mn).Citation
NIST Interagency/Internal Report (NISTIR) - 8066
Report Number
8066
NIST Pub Series
Pub Type
NIST Pubs
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Keywords
random graphs, degree sequence, graph algorithms
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Created January 6, 2016, Updated November 10, 2018