We review results on the scaling of the optimal path length l(opt) in random networks with weighted links or nodes. We refer to such networks as "weighted" or "disordered" networks. The optimal path is the path with minimum sum of the weights. In strong disorder, where the maximal weight along...

We review the analysis of the length of the optimal path ℓopt 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 ℓopt increases dramatically compared to the known...

We study the effects of relaxational dynamics on congestion pressure in scale free networks by analyzing the properties of the corresponding gradient networks (Z. Toroczkai, K. E. Bassler, Nature bf 428, 716 (2004)). Using the Family model (F. Family, J. Phys. A, bf 19, L441 (1986)) from...

We study the stability of network communication after removal of a fraction q=1-p of links under the assumption that communication is effective only if the shortest path between nodes i and j after removal is shorter than aℓij(a≥1) where ℓij is the shortest path before removal. For a large...

In this paper, we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oilfield to breakthrough into a production well. The main contribution is to show that when these previously published results are used on realistic data they are in...

In this paper, we apply scaling laws from percolation theory to the problem of estimating the time for a fluid injected into an oil field to breakthrough into a production well. The main contribution is to show that when these previously published results are used on realistic data they are in...

We numerically simulate the traveling time of a tracer in convective flow between two points (injection and extraction) separated by a distance r in a model of porous media, d=2 percolation. We calculate and analyze the traveling time probability density function for two values of the fraction...

We study numerically the optimal paths in two and three dimensions on various disordered lattices in the limit of strong disorder. We find that the length l of the optimal path scales with geometric distance r , as l approximately r (d(opt) with d(opt) =1.22+/-0.01 for d=2 and 1.44+/-0.02 for...

We study the current flow paths between two edges in a random resistor network on a Ltimes L square lattice. Each resistor has resistance e ax, where x is a uniformly-distributed random variable and a controls the broadness of the distribution. We find (a) the scaled variable uequiv L/a nu,...

To study transport properties of complex networks, we analyze the equivalent conductance G between two arbitrarily chosen nodes of random scale-free networks with degree distribution P(k)sim k -lambda in which each link has the same unit resistance. We predict a broad range of values of G, with...