Shortest paths and load scaling in scale-free trees
Statistical Mechanics
2009-11-07 v2 Disordered Systems and Neural Networks
Abstract
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering mean-field arguments and by mapping the m=1 case of the Barabasi-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows a demonstration of why the distribution approaches a Gaussian in the limit of N large. The load (betweenness), the number of shortest distance paths passing through any node, is discussed in the tree presentation.
Cite
@article{arxiv.cond-mat/0203278,
title = {Shortest paths and load scaling in scale-free trees},
author = {Gabor Szabo and Mikko Alava and Janos Kertesz},
journal= {arXiv preprint arXiv:cond-mat/0203278},
year = {2009}
}
Comments
8 pages, 8 figures; v2: load calculations extended