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May 9, 2026Theory of Probability and Its Applications0 citations

On the Maximal Degree of a Vertex of a Conditional Configuration Graph

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ICI.A. Cheplyukova

Key Points

  • The aim is to determine the behavior of the maximal degree of vertices in a configuration graph with random vertex degrees.
  • Analyzed a model of N-vertex configuration graph where vertex degrees are i.i.d. random variables.
  • Characterized the distribution of vertex degrees satisfying a specific power-law condition.
  • Proved limit theorem under the condition that N and n approach infinity with a defined relationship.
  • Established that the maximal degree behaves according to the derived limit theorem as N, n → ∞.
  • Found necessary conditions involving h(N) and n for the theorem to hold, specifying a lower bound C > 0.

Abstract

We consider the model of an N-vertex configuration graph, where the degrees of vertices are independent and identically distributed random variables, and the distribution of the random variable, which is the degree of each vertex, satisfies the condition pₖ=P\=k\ h (k) kᵍ, 20.

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Cite This Study

I.A. Cheplyukova (2026) studied this question.

synapsesocial.com/papers/69fecf71b9154b0b82876635https://doi.org/10.1137/s0040585x97t992768
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