# zbMATH — the first resource for mathematics

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
##### Keywords:
large data transmission networks
Full Text:
##### References:
 [1] Pavlov Yu. L., Discrete Math. Appl. 18 pp 447– (2008) · Zbl 1171.05419 · doi:10.1515/DMA.2008.033 [2] Reittu H., Performance Evaluation 55 pp 3– (2004) · doi:10.1016/S0166-5316(03)00097-X [3] Faloutsos C., Computer Communications Rev. 29 pp 251– (1999) · doi:10.1145/316194.316229 [4] Newman M. E. J., Phys. Rev. E 64 pp 026118– (2001) · doi:10.1103/PhysRevE.64.026118 [5] Yu., Discrete Math. Appl. 17 pp 425– (2007) · Zbl 1247.05220 · doi:10.1515/dma.2007.034 [6] Robinson J. E., Phys. Rev. 2 83 pp 678– (1951) · Zbl 0042.44302 · doi:10.1103/PhysRev.83.678 [7] Kolchin A. V., Discrete Math. Appl. 13 pp 627– (2003) · Zbl 1046.60019 · doi:10.1515/156939203322733336 [8] Mukhin A. B., Theory Probab. Appl. 36 pp 698– (1991) · Zbl 0776.60027 · doi:10.1137/1136086
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.