Uncorrelated Random Networks

Details Uncorrelated Random Networks Uncorrelated Random Networks

2002-06-30

arxiv.org/abs/cond-mat/0207020v3

Phys. Rev. E 67, 046118 (2003)

Physics

Condensed Matter

Statistical Mechanics

7 pages, 4 eps figures, 2-column revtex format, final corrections before publication

Scientific paper

10.1103/PhysRevE.67.046118

We define a statistical ensemble of non-degenerate graphs, i.e. graphs without multiple- and self-connections between nodes. The node degree distribution is arbitrary, but the nodes are assumed to be uncorrelated. This completes our earlier publication \cite{bck}, where trees and degenerate graphs were considered. An efficient algorithm generating non-degenerate graphs is constructed. The corresponding computer code is available on request. Finite-size effects in scale-free graphs, i.e. those where the tail of the degree distribution falls like $n^{-\beta}$, are carefully studied. We find that in the absence of dynamical internode correlations the degree distribution is cut at a degree value scaling like $N^{\gamma}$, with $\gamma = \min[1/2, 1/(\beta-1)]$, where $N$ is the total number of nodes. The consequence is that, independently of any specific model, the inter-node correlations seem to be a necessary ingredient of the physics of scale-free networks observed in nature.

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