Walks on weighted networks

Abstract

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.

4 pages, 5 figures. minor modifications. Comments and suggestions are favored by the authors

References in corpus (18)

• Emergence of scaling in random networks
• The structure and function of complex networks
• The architecture of complex weighted networks
• Evolution of networks
• Search in Power-Law Networks
• Weighted evolving networks: coupling topology and weights dynamics
• Modeling the evolution of weighted networks
• Epidemic spread in weighted scale-free networks
• Exploring complex networks by walking on them
• Rate equation approach for correlations in growing network models
• Random spread on the family of small-world networks
• Scaling Properties of Random Walks on Small-World Networks
• Random walk and trapping processes on scale-free networks
• Scaling of random spreading in small world networks
• Diffusion and networks: A powerful combination!
• Constrained spin dynamics description of random walks on hierarchical scale-free networks
• Traversal Times for Random Walks on Small-World Networks
• Random Walks on Complex Networks

Cited by in corpus (7)

• Random walks on weighted networks
• Mean-field diffusive dynamics on weighted networks
• Random walks in weighted networks with a perfect trap: An application of Laplacian spectra
• Voter models on weighted networks
• Correlations between structure and dynamics in complex networks
• Phase-Space Networks of Geometrical Frustrated Systems
• Time-varying networks approach to social dynamics: From individual to collective behavior