Geodesic
On the asymptotics of degree structure of configuration graphs with bounded number of edges
Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 77-94.

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We consider configuration graphs with $N$ vertices. The degrees of vertices are independent identically distributed random variables having the power-law distribution with positive parameter $\tau$. We study properties of random graphs such that the sum of vertex degrees does not exceed $n$ and the parameter $\tau$ is a random variable uniformly distributed on the interval $[a,b], 0$. We find limit distributions of the number $\mu_r$ of vertices with degree $r$ for various types of variation of $N,n$ and $r$.
Keywords: configuration graph, vertex degree, limit distribution. 
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Yu. L. Pavlov; I. A. Cheplyukova. On the asymptotics of degree structure of configuration graphs with bounded number of edges. Diskretnaya Matematika, Tome 30 (2018) no. 1, pp. 77-94. http://geodesic.mathdoc.fr/item/DM_2018_30_1_a5/

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