Walks on weighted networks

We investigate the dynamics of random walks on weighted networks. Assuming that the edge's weight and the node's strength are used as local information by a random walker, we study two kinds of walks, weight-dependent walk and strength-dependent walk. Exact expressions for stationary distribution and average return time are derived and confirmed by computer simulations. We calculate the distribution of average return time and the mean-square displacement for two walks on the BBV networks, and find that a weight-dependent walker can arrive at a new territory more easily than a strength-dependent one.