Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9728040 | Physica A: Statistical Mechanics and its Applications | 2005 | 11 Pages |
Abstract
We review the analysis of the length of the optimal path âopt in random networks with disorder (i.e., random weights on the links). In the case of strong disorder, in which the maximal weight along the path dominates the sum, we find that âopt increases dramatically compared to the known small-world result for the minimum distance âmin: for ErdÅs-Rényi (ER) networks âoptâ¼N1/3, while for scale-free (SF) networks, with degree distribution P(k)â¼k-λ, we find that âopt scales as N(λ-3)/(λ-1) for 3<λ<4 and as N1/3 for λ⩾4. Thus, for these networks, the small-world nature is destroyed. For 2<λ<3, our numerical results suggest that âopt scales as lnλ-1N. We also find numerically that for weak disorder âoptâ¼lnN for ER models as well as for SF networks. We also study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path âopt in ER and SF networks.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Shlomo Havlin, Lidia A. Braunstein, Sergey V. Buldyrev, Reuven Cohen, Tomer Kalisky, Sameet Sreenivasan, H. Eugene Stanley,