Pseudofractal Scale-free Web
摘要
We find that scale-free random networks are excellently modeled by a deterministic graph. This graph has a discrete degree distribution (degree is the number of connections of a vertex) which is characterized by a power-law with exponent . Properties of this simple structure are surprisingly close to those of growing random scale-free networks with in the most interesting region, between 2 and 3. We succeed to find exactly and numerically with high precision all main characteristics of the graph. In particular, we obtain the exact shortest-path-length distribution. For the large network () the distribution tends to a Gaussian of width centered at . We show that the eigenvalue spectrum of the adjacency matrix of the graph has a power-law tail with exponent .
引用
@article{arxiv.cond-mat/0112143,
title = {Pseudofractal Scale-free Web},
author = {S. N. Dorogovtsev and A. V. Goltsev and J. F. F. Mendes},
journal= {arXiv preprint arXiv:cond-mat/0112143},
year = {2009}
}
备注
5 pages, 3 figures