Organization of Growing Random Networks

Details Organization of Growing Random Networks Organization of Growing Random Networks

2000-11-06

arxiv.org/abs/cond-mat/0011094v2

Phys. Rev. E 63, 066123-1--066123-14 (2001)

Physics

Condensed Matter

Statistical Mechanics

14 pages, 6 figures, 2-column revtex format final version for PRE; minor revisions and some references added

Scientific paper

10.1103/PhysRevE.63.066123

The organizational development of growing random networks is investigated. These growing networks are built by adding nodes successively and linking each to an earlier node of degree k with attachment probability A_k. When A_k grows slower than linearly with k, the number of nodes with k links, N_k(t), decays faster than a power-law in k, while for A_k growing faster than linearly in k, a single node emerges which connects to nearly all other nodes. When A_k is asymptotically linear, N_k(t) tk^{-nu}, with nu dependent on details of the attachment probability, but in the range 2

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