Scaling of optimal-path-lengths distribution in complex networks

Tomer Kalisky, Lidia A. Braunstein, Sergey V. Buldyrev, Shlomo Havlin, H. Eugene Stanley

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11 Scopus citations


We study the distribution of optimal path lengths in random graphs with random weights associated with each link ("disorder"). With each link i we associate a weight τi=exp(ari), where ri is a random number taken from a uniform distribution between 0 and 1, and the parameter a controls the strength of the disorder. We suggest, in an analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form that is controlled by the expression (1pc)(a), where is the optimal path length in strong disorder (a→) and pc is the percolation threshold. This relation is supported by numerical simulations for Erdos-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network.

Original languageEnglish
Article number025102
JournalPhysical Review E
Issue number2
StatePublished - Aug 2005


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