Size-dependent degree distribution of a scale-free growing network.
We propose the simplest model of scale-free growing networks and obtain the exact form of its degree distribution for any size of the network (degree is a number of connections of a node). We demonstrate that a trace of initial conditions - a hump near cutoff of the degree distribution at k(cut) approximately t(beta)--may be found for any network size. Here beta=1/(gamma-1), where gamma is the exponent of the degree distribution of the network. These size effects implement a natural boundary for the observation of the scale-free networks.
Dorogovtsev
S N
SN
Departamento de Física, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal. sdorogov@fc.up.pt
Mendes
J F
JF
Samukhin
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AN