Shifting the Link Weights in Networks

Transport in large networks follows near to shortest paths. A shortest path depends on the topology as well as on the link weight structure. While much effort has been devoted to understand the properties of the topology of large networks, the influence of link weights on the shortest path received considerably less attention. The scaling of all link weights in a graph by a positive number does not change the shortest path and most of the link weight distributions can be generated as a function of the uniform distribution. Hence, we compute analytically and by simulation the effect of shifting the uniform distribution for the link weights from [0,1] to (a,1] where 1 ≫ a ≫ 0. The properties of the shortest path (hopcount and weight) vary for different a as well as the topology. Furthermore, when a is large, the traffic is more likely to follow the minimum hopcount shortest path, which leads to more balanced traffic traversing the network.