Optimal Paths in Disordered Complex Networks

Simple item page
dc.creatorBraunstein, Lidia A.
dc.creatorBuldyrev, Sergey V.
dc.creatorCohen, Reuven
dc.creatorHavlin, Shlomo
dc.creatorStanley, H. Eugene
dc.date2003-05-03
dc.date2003-08-26
dc.date.accessioned2026-07-07T02:51:09Z
dc.date.available2026-07-07T02:51:09Z
dc.descriptionWe study the optimal distance in networks, $\ell_{\scriptsize opt}$, 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 $\ell_{\scriptsize opt}\sim N^{1/3}$ in both Erdős-Rényi (ER) and Watts-Strogatz (WS) networks. For scale free (SF) networks, with degree distribution $P(k) \sim k^{-λ}$, we find that $\ell_{\scriptsize opt}$ scales as $N^{(λ- 3)/(λ- 1)}$ for $3<λ<4$ and as $N^{1/3}$ for $λ\geq 4$. Thus, for these networks, the small-world nature is destroyed. For $2 < λ< 3$, our numerical results suggest that $\ell_{\scriptsize opt}$ scales as $\ln^{λ-1}N$. We also find numerically that for weak disorder $\ell_{\scriptsize opt}\sim\ln N$ for both the ER and WS models as well as for SF networks.
dc.description5 pages, 4 figures, accepted for publication in Physical Review Letters
dc.identifierhttps://arxiv.org/abs/cond-mat/0305051
dc.identifierhttp://arxiv.org/abs/cond-mat/0305051
dc.identifierPhys. Rev. Lett. 91, 168701 (2003)
dc.identifierdoi:10.1103/PhysRevLett.91.168701
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/21347
dc.subjectSoft Condensed Matter
dc.titleOptimal Paths in Disordered Complex Networks
dc.typetext

Files

Collections

arXiv