Shortest paths and load scaling in scale-free trees

Details Shortest paths and load scaling in scale-free trees Shortest paths and load scaling in scale-free trees

2002-03-13

arxiv.org/abs/cond-mat/0203278v2

Phys. Rev. E 66, 026101 (2002)

Physics

Condensed Matter

Statistical Mechanics

8 pages, 8 figures; v2: load calculations extended

Scientific paper

10.1103/PhysRevE.66.026101

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.

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