Load-dependent random walks on complex networks

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.