Scaling of optimal-path-lengths distribution in complex networks
| dc.creator | Kalisk, Tomer | |
| dc.creator | Braunstein, Lidia A. | |
| dc.creator | Buldyrev, Sergey V. | |
| dc.creator | Havlin, Shlomo | |
| dc.creator | Stanley, H. Eugene | |
| dc.date | 2005-08-01 | |
| dc.date.accessioned | 2026-07-07T03:06:11Z | |
| dc.date.available | 2026-07-07T03:06:11Z | |
| dc.description | We study the distribution of optimal path lengths in random graphs with random weights associated with each link (``disorder''). With each link $i$ we associate a weight $τ_i = \exp(ar_i)$ 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 suggest, in analogy with the average length of the optimal path, that the distribution of optimal path lengths has a universal form which is controlled by the expression $\frac{1}{p_c}\frac{\ell_{\infty}}{a}$, where $\ell_{\infty}$ is the optimal path length in strong disorder ($a \to \infty$) and $p_c$ is the percolation threshold. This relation is supported by numerical simulations for Erdős-Rényi and scale-free graphs. We explain this phenomenon by showing explicitly the transition between strong disorder and weak disorder at different length scales in a single network. | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0508039 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0508039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/26717 | |
| dc.subject | Disordered Systems and Neural Networks | |
| dc.title | Scaling of optimal-path-lengths distribution in complex networks | |
| dc.type | text |