Abstract
We consider configuration graphs under the condition that the sum of vertex degrees is bounded from above by n. The vertex degrees are independent identically distributed random variables. The distribution of the vertex degree ξ is unknown and has the only limiting condition that P{ξ=k} пропорционально d/( k g ln h k), where d>0, g>1, h≥0. We obtained the limit distributions of the maximum vertex degree as the number of graph vertices and n tends to infinity.
Highlights
D kg(ln k)h, где d > 0, g > 1, h 0
We obtained the limit distributions of the maximum vertex degree as the number of graph vertices and n tends to infinity
On the power-law random graph model of massive data networks // Performance Evaluation
Summary
3, где Γ(x)− значение гамма-функции в точке x. 0 < γ < ∞, ε – некоторая положительная постоянная и выполнено одно из условий: 1. G = 2, h 1, (n − d ln1−h N (1 + ε)N )/BN → ∞; 3. I0(x)– плотность устойчивого закона с показателем g − 1 и характеристической функцией exp.
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