Limit theorems for the weights and the degrees in anN-interactions random graph model
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Abstract A random graph evolution based on interactions of N vertices is studied. During the evolution both the preferential attachment rule and the uniform choice of vertices are allowed. The weight of an M-clique means the number of its interactions. The asymptotic behaviour of the weight of a fixed M-clique is studied. Asymptotic theorems for the weight and the degree of a fixed vertex are also presented. Moreover, the limits of the maximal weight and the maximal degree are described. The proofs are based on martingale methods.
2013 ◽
Vol 2013
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pp. 1-12
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2009 ◽
Vol 12
(01)
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pp. 45-71
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2019 ◽
Vol 29
(1)
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pp. 35-61
2018 ◽
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2020 ◽
Vol 29
(6)
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pp. 830-867
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