Random walks on weighted networks: a survey of local and non-local dynamics

@article{Riascos2021RandomWO,
  title={Random walks on weighted networks: a survey of local and non-local dynamics},
  author={Alejandro P. Riascos and Jos{\'e} L. Mateos},
  journal={J. Complex Networks},
  year={2021},
  volume={9}
}
In this article, we present a survey of different types of random walk models with local and non-local transitions on undirected weighted networks. We present a general approach by defining the dynamics as a discrete-time Markovian process with transition probabilities expressed in terms of a symmetric matrix of weights. In the first part, we describe the matrices of weights that define local random walk dynamics like the normal random walk, biased random walks and preferential navigation… 

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References

SHOWING 1-10 OF 145 REFERENCES

Random walks with long-range steps generated by functions of Laplacian matrices

In this paper, we explore different Markovian random walk strategies on networks with transition probabilities between nodes defined in terms of functions of the Laplacian matrix. We generalize

Mean First Passage Time of Preferential Random Walks on Complex Networks with Applications

This paper investigates, both theoretically and numerically, preferential random walks (PRW) on weighted complex networks. By using two different analytical methods, two exact expressions are derived

Lévy random walks on multiplex networks

This work derives analytical expressions for the mean first passage time and the average time to reach a node on multiplex networks from spectral graph and stochastic matrix theories and finds that in some region of the parameters, a Lévy random walk is the most efficient strategy.

Random Walks on Graphs: a Survey

Dedicated to the marvelous random walk of Paul Erd} os through universities, c ontinents, and mathematics Various aspects of the theory of random walks on graphs are surveyed. In particular,

Biased random walks on multiplex networks

This work introduces biased random walks on multiplex networks and provides analytical solutions for their long-term properties such as the stationary distribution and the entropy rate, and distinguishes between two subclasses of random walks.

Fractional random walk lattice dynamics

We analyze time-discrete and time-continuous ‘fractional’ random walks on undirected regular networks with special focus on cubic periodic lattices in n  =  1, 2, 3,.. dimensions. The fractional

Biased random walks in complex networks: the role of local navigation rules.

  • A. FronczakP. Fronczak
  • Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2009
The biased random-walk process in random uncorrelated networks with arbitrary degree distributions is studied to provide the basis for a theoretical treatment of transport-related problems in complex networks, including quantitative estimation of the critical value of the packet generation rate.

Random walks in weighted networks with a perfect trap: an application of Laplacian spectra.

  • Yuan LinZhongzhi Zhang
  • Mathematics, Computer Science
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
This paper proposes a general framework for the trapping problem on a weighted network with a perfect trap fixed at an arbitrary node, and deduces an explicit expression for average trapping time (ATT) in terms of the eigenvalues and eigenvectors of the Laplacian matrix associated with the weighted graph.

Fractional dynamics on networks: emergence of anomalous diffusion and Lévy flights.

The general fractional diffusion formalism applies to regular, random, and complex networks and can be implemented from the spectral properties of the Laplacian matrix, providing an important tool to analyze anomalous diffusion on networks.
...