TY - JOUR

T1 - Scaling of optimal-path-lengths distribution in complex networks

AU - Kalisky, Tomer

AU - Braunstein, Lidia A.

AU - Buldyrev, Sergey V.

AU - Havlin, Shlomo

AU - Stanley, H. Eugene

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=27244447435&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.72.025102

DO - 10.1103/PhysRevE.72.025102

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C2 - 16196625

AN - SCOPUS:27244447435

SN - 1539-3755

VL - 72

JO - Physical Review E

JF - Physical Review E

IS - 2

M1 - 025102

ER -