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On the limit distribution of the number of cycles in a random graph

Published online by Cambridge University Press:  14 July 2016

Lajos Takács
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Abstract

Let Γn(p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where . Denote by γ n(p) the total number of cycles in the graph Γn(p). The main object of this paper is to prove that the limit distribution of γ n(λ /n) is a Poisson distribution with expectation if n → ∞and 0 < λ< 1.

Keywords

GRAPH THEORYCYCLESPOISSON DISTRIBUTION
Type
Part 8 - Random Walks, Graphs and Networks
Information
Journal of Applied Probability , Volume 25 , Issue A , 1988 , pp. 359 - 376
Copyright
Copyright © Applied Probability Trust 1988 

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