Characterizing the structure of small-world networks

Details Characterizing the structure of small-world networks Characterizing the structure of small-world networks

2001-09-13

arxiv.org/abs/cond-mat/0109227v1

Phys. Rev. Lett. 88, 098101 (2002).

Physics

Condensed Matter

Disordered Systems and Neural Networks

Scientific paper

10.1103/PhysRevLett.88.098101

We give exact relations which are valid for small-world networks (SWN's) with a general `degree distribution', i.e the distribution of nearest-neighbor connections. For the original SWN model, we illustrate how these exact relations can be used to obtain approximations for the corresponding basic probability distribution. In the limit of large system sizes and small disorder, we use numerical studies to obtain a functional fit for this distribution. Finally, we obtain the scaling properties for the mean-square displacement of a random walker, which are determined by the scaling behavior of the underlying SWN.

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