Effect of disorder strength on optimal paths in complex networks

Sameet Sreenivasan; Tomer Kalisky; Lidia A. Braunstein; Sergey V. Buldyrev; Shlomo Havlin; H. Eugene Stanley

doi:10.1103/PhysRevE.70.046133

Effect of disorder strength on optimal paths in complex networks

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

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Abstract

The transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l_opt in a disordered Erdös-Rényi (ER) random network and scale-free (SF) networks was studied. Each link i was associated with a weight τ_i≡ exp(ar_i), where i is a random number taken from a uniform distribution between 0 and 1 and the strength of the disorder is controlled by the parameter 'a'. It was found that for any finite 'a', there was a crossover network size N*(a) , at which the transition occurred. A measure which indicated how close or far the disordered network is from the limit of the strong disorder was also proposed.

Original language	English
Article number	046133
Pages (from-to)	046133-1-046133-6
Journal	Physical Review E
Volume	70
Issue number	4 2
DOIs	https://doi.org/10.1103/PhysRevE.70.046133
State	Published - Oct 2004

Bibliographical note

Funding Information:
The authors thank the Office of Naval Research, the Israel Science Foundation, and the Israeli Center for Complexity Science for financial support, and R. Cohen, E. Lopez, E. Perlsman, G. Paul, T. Tanizawa, and Z. Wu for discussions.

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10.1103/PhysRevE.70.046133

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title = "Effect of disorder strength on optimal paths in complex networks",

abstract = "The transition between the strong and weak disorder regimes in the scaling properties of the average optimal path lopt in a disordered Erd{\"o}s-R{\'e}nyi (ER) random network and scale-free (SF) networks was studied. Each link i was associated with a weight τi≡ exp(ari), where i is a random number taken from a uniform distribution between 0 and 1 and the strength of the disorder is controlled by the parameter 'a'. It was found that for any finite 'a', there was a crossover network size N*(a) , at which the transition occurred. A measure which indicated how close or far the disordered network is from the limit of the strong disorder was also proposed.",

author = "Sameet Sreenivasan and Tomer Kalisky and Braunstein, {Lidia A.} and Buldyrev, {Sergey V.} and Shlomo Havlin and Stanley, {H. Eugene}",

note = "Funding Information: The authors thank the Office of Naval Research, the Israel Science Foundation, and the Israeli Center for Complexity Science for financial support, and R. Cohen, E. Lopez, E. Perlsman, G. Paul, T. Tanizawa, and Z. Wu for discussions.",

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doi = "10.1103/PhysRevE.70.046133",

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AU - Havlin, Shlomo

AU - Stanley, H. Eugene

N1 - Funding Information: The authors thank the Office of Naval Research, the Israel Science Foundation, and the Israeli Center for Complexity Science for financial support, and R. Cohen, E. Lopez, E. Perlsman, G. Paul, T. Tanizawa, and Z. Wu for discussions.

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Effect of disorder strength on optimal paths in complex networks

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