  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.
