title: Optimal paths in disordered complex networks.
abstract: We study the optimal distance in networks, l(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 l(opt) approximately N(1/3) in both Erdos-Rényi (ER) and Watts-Strogatz (WS) networks. For scale-free (SF) networks, with degree distribution P(k) approximately k(-lambda), we find that l(opt) scales as N((lambda-3)/(lambda-1)) for 3<lambda<4 and as N(1/3) for lambda> or =4. Thus, for these networks, the small-world nature is destroyed. For 2<lambda<3, our numerical results suggest that l(opt) scales as ln(lambda-1N. We also find numerically that for weak disorder l(opt) approximately ln(N for both the ER and WS models as well as for SF networks.
authors: Center for Polymer Studies and Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
authors: Lidia A
authors: LA
authors: Braunstein
authors: Sergey V
authors: SV
authors: Buldyrev
authors: Reuven
authors: R
authors: Cohen
authors: Shlomo
authors: S
authors: Havlin
authors: H Eugene
authors: HE
authors: Stanley
mesh_terms: D003142:Communication; D008954:Models, Biological; D008962:Models, Theoretical; D012944:Social Support