کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9728040 | 1480216 | 2005 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Optimal path in random networks with disorder: A mini review
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
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چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Physica A: Statistical Mechanics and its Applications - Volume 346, Issues 1â2, 1 February 2005, Pages 82-92
Journal: Physica A: Statistical Mechanics and its Applications - Volume 346, Issues 1â2, 1 February 2005, Pages 82-92
نویسندگان
Shlomo Havlin, Lidia A. Braunstein, Sergey V. Buldyrev, Reuven Cohen, Tomer Kalisky, Sameet Sreenivasan, H. Eugene Stanley,