Organization of complex networks without multiple connections

Details Organization of complex networks without multiple connections Organization of complex networks without multiple connections

2005-05-08

arxiv.org/abs/cond-mat/0505193v2

Phys.Rev.Lett. 95 (2005) 195701

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures

Scientific paper

10.1103/PhysRevLett.95.195701

We find a new structural feature of equilibrium complex random networks without multiple and self-connections. We show that if the number of connections is sufficiently high, these networks contain a core of highly interconnected vertices. The number of vertices in this core varies in the range between $const N^{1/2}$ and $const N^{2/3}$, where $N$ is the number of vertices in a network. At the birth point of the core, we obtain the size-dependent cut-off of the distribution of the number of connections and find that its position differs from earlier estimates.

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