Shortest paths and load scaling in scale-free trees

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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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Artikkeli026101
Sivut1-8
JulkaisuPhysical Review E
Vuosikerta66
Numero2
TilaJulkaistu - 2002
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 3480933