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On the limit distributions of the vertex degrees of conditional internet graphs. (English. Russian original) Zbl 1237.05194
Discrete Math. Appl. 19, No. 4, 349-359 (2009); translation from Diskretn. Mat. 21, No. 3, 14-23 (2009).
Summary: We consider the random graphs modelling the structure of large data transmission networks including Internet. We investigate the subset of such graphs consisting of \(N\) vertices under the condition that the number of edges is equal to \(n\). We obtain the limit distributions of the maximum degree of vertices and the number of vertices of a given degree as \(N, n \rightarrow \infty \) so that \( n/ N \rightarrow \lambda \), where \(\lambda \) is a positive constant.

MSC:
05C82 Small world graphs, complex networks (graph-theoretic aspects)
05C80 Random graphs (graph-theoretic aspects)
05C07 Vertex degrees
68M11 Internet topics
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