Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2004-05-10
Physics
Condensed Matter
Disordered Systems and Neural Networks
6 pages, 6 figures. submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.70.046133
We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path $\ell_{\rm opt}$ in a disordered Erd\H{o}s-R\'enyi (ER) random network and scale-free (SF) network. Each link $i$ is associated with a weight $\tau_i\equiv\exp(a r_i)$, where $r_i$ is a random number taken from a uniform distribution between 0 and 1 and the parameter $a$ controls the strength of the disorder. We find that for any finite $a$, there is a crossover network size $N^*(a)$ at which the transition occurs. For $N \ll N^*(a)$ the scaling behavior of $\ell_{\rm opt}$ is in the strong disorder regime, with $\ell_{\rm opt} \sim N^{1/3}$ for ER networks and for SF networks with $\lambda \ge 4$, and $\ell_{\rm opt} \sim N^{(\lambda-3)/(\lambda-1)}$ for SF networks with $3 < \lambda < 4$. For $N \gg N^*(a)$ the scaling behavior is in the weak disorder regime, with $\ell_{\rm opt}\sim\ln N$ for ER networks and SF networks with $\lambda > 3$. In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between $N^*(a)$ and $a$. We find that $N^*(a)\sim a^3$ for ER networks and for SF networks with $\lambda\ge 4$, and $N^*(a)\sim a^{(\lambda-1)/(\lambda-3)}$ for SF networks with $3 < \lambda < 4$.
Braunstein Lidia A.
Buldyrev Sergey V.
Havlin Shlomo
Kalisky Tomer
Sreenivasan Sameet
No associations
LandOfFree
Effect of Disorder Strength on Optimal Paths in Complex Networks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Effect of Disorder Strength on Optimal Paths in Complex Networks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Effect of Disorder Strength on Optimal Paths in Complex Networks will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-20724