Shortest paths and load scaling in scale-free trees

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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 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 Barabási-Albert model into a tree with a depth-dependent branching ratio. This shows the origins of the average distance scaling and allows one to demonstrate why the distribution approaches a Gaussian in the limit of N large. The load, the number of the shortest distance paths passing through any node, is discussed in the tree presentation.

Details

Original languageEnglish
Article number026101
Pages (from-to)1-8
JournalPhysical Review E
Volume66
Issue number2
Publication statusPublished - 2002
MoE publication typeA1 Journal article-refereed

ID: 3480933