Shortest paths and load scaling in scale-free trees

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  • 13 March 2002
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 the pdf 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, the number of shortest distance paths passing through any node, is discussed in the tree presentation.

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