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 -