Abstract
We investigate the dynamics of random walks on weighted networks.Assuming that the edge weight and the node strength are usedas local information by a random walker. Two kinds of walks,weight-dependent walk and strength-dependent walk, are studied. Exactexpressions for stationary distribution and average return time arederived and confirmed by computer simulations. The distribution ofaverage return time and the mean-square displacement are calculated fortwo walks on the Barrat–Barthélemy–Vespignani (BBV) networks. Itis found that a weight-dependent walker can arrive at a new territorymore easily than a strength-dependent one.
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