Jamming in the weighted gradient networks

We introduce a weighted gradient network on the unweighted substrate networks. The edge weight w i j is defined as the power-law function of the scalar difference | h j − h i | between the two connected nodes i and j , i.e., w i j ∼ | h j − h i | α . The jamming factor J of the whole network is defined as the average of the jamming degrees of all nodes. The jamming properties are studied for the substrate of random and scale-free networks. We find a crossover phenomenon in two networks. For α > α c ( α c denotes a critical parameter, estimated to be about 1.5 for the random network and about 2.0 for the scale-free network), the value of J increases with increasing average connectivity 〈 k 〉 of the network, while for α < α c , the reverse occurs. In addition, the jamming effects of the two networks are compared, and we give the range of values of α and 〈 k 〉 that the scale-free networks have a higher level of congestion than the random networks.