Network navigation with non-Lèvy superdiffusive random walks
EntityUAM. Departamento de Ingeniería Informática
10.1016/j.physa.2021.126158Physica A 580.(2021): 126158
Funded bySimone Santini was supported in part by the Spanish Ministerio de Ciencia e Innovación under the grant N. PID2019-108965GB-I00 Más allá de la recomendación estática: equidad, interacción y transparencia
ProjectGobierno de España. PID2019-108965GB-I00
Rights© 2021 by the authors
Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
We introduce a formalism based on a continuous time approximation to study the characteristics of random walks with jumps to random locations of the networks (Pagerank random walks). We find that the diffusion of the occupancy probability has a dynamics that exponentially “forgets” the initial conditions and settles to a steady state that depends only on the characteristics of the network. In the special case in which the walk begins from a single node, we show that the largest eigenvalue of the transition value (λ1=1) does not contribute to the dynamic and that the probability is constant in the direction of the corresponding eigenvector. We study the process of visiting new nodes, which we find to have a dynamic similar to that of the occupancy probability. Finally, we determine the average transit time between nodes 〈T〉. We show that, for suitable values of the walk parameters, Pagerank walks behave similarly to Lèvy walks in terms of unique nodes visited and average transit time, while requiring much less information about the graph
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