Random walks on weighted networks: a survey of local and non-local dynamics
Por:
Riascos, A. P., Mateos, Jose L.
Publicada:
18 sep 2021
Resumen:
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, random walks in the context of digital image processing and
maximum entropy random walks. In addition, we explore non-local random
walks, like Levy flights on networks, fractional transport through the
new formalism of fractional graph Laplacians, and applications in the
context of human mobility. Explicit relations for the stationary
probability distribution, the mean first passage time and global times
to characterize random walks are obtained in terms of the elements of
the matrix of weights and its respective eigenvalues and eigenvectors.
Finally, we apply the results to the analysis of particular local and
non-local random walk dynamics, and we discuss their capacity to explore
several types of networks. Our results allow us to study and compare the
global dynamics of different types of random walk models.
Filiaciones:
Riascos, A. P.:
Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México, 01000, Mexico
Univ Nacl Autonoma Mexico, Inst Fis, Apartado Postal 20-364, Ciudad De Mexico 01000, Mexico
Mateos, Jose L.:
Instituto de Física, Universidad Nacional Autónoma de México, Apartado Postal 20-364, Ciudad de México, 01000, Mexico
Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México, Apartado Postal 04510, Ciudad de México, Mexico
Univ Nacl Autonoma Mexico, Inst Fis, Apartado Postal 20-364, Ciudad De Mexico 01000, Mexico
Univ Nacl Autonoma Mexico, Ctr Ciencias Complejidad, Apartado Postal 04510, Ciudad De Mexico, Mexico
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