Optimal paths in disordered complex networks.

Lidia A Braunstein; Sergey V Buldyrev; Reuven Cohen; Shlomo Havlin; H Eugene Stanley

doi:10.1103/physrevlett.91.168701

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Optimal paths in disordered complex networks.

Lidia A Braunstein·Sergey V Buldyrev·Reuven Cohen·Shlomo Havlin·H Eugene Stanley

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Abstract

We study the optimal distance in networks, l(opt), defined as the length of the path minimizing the total weight, in the presence of disorder. Disorder is introduced by assigning random weights to the links or nodes. For strong disorder, where the maximal weight along the path dominates the sum, we find that l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3 or =4. Thus, for these networks, the small-world nature is destroyed. For 2<lambda<3, our numerical results suggest that l(opt) scales as ln(lambda-1N. We also find numerically that for weak disorder l(opt) approximately ln(N for both the ER and WS models as well as for SF networks.

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Communication Models, Biological Models, Theoretical Social Support Journal Article Research Support, Non-U.S. Gov't Research Support, U.S. Gov't, Non-P.H.S.

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Lidia A Braunstein, Sergey V Buldyrev, Reuven Cohen, Shlomo Havlin, H Eugene Stanley. 2003-10-17. Optimal paths in disordered complex networks.. https://doi.org/10.1103/physrevlett.91.168701

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