Shortest paths and load scaling in scale-free trees

Gabor Szabo; Mikko Alava; Janos Kertesz

doi:10.1103/physreve.66.026101

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Shortest paths and load scaling in scale-free trees

Gabor Szabo·Mikko Alava·Janos Kertesz

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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.

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Gabor Szabo, Mikko Alava, Janos Kertesz. 2002-05-08. Shortest paths and load scaling in scale-free trees. https://doi.org/10.1103/physreve.66.026101

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