Journal of Applied Probability

The probability that a random multigraph is simple. II

Svante Janson


Consider a random multigraph G* with given vertex degrees d1, . . ., dn, constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges ½∑idi → ∞, the probability that the multigraph is simple stays away from 0 if and only if ∑idi = O(∑idi). The new proof uses the method of moments, which makes it possible to use it in some applications concerning convergence in distribution. Corresponding results for bipartite graphs are included.

Article information

J. Appl. Probab., Volume 51A (2014), 123-137.

First available in Project Euclid: 2 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C80: Random graphs [See also 60B20] 05C30: Enumeration in graph theory 60C05: Combinatorial probability

Configuration model random multigraph random bipartite graph


Janson, Svante. The probability that a random multigraph is simple. II. J. Appl. Probab. 51A (2014), 123--137. doi:10.1239/jap/1417528471.

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