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Network navigation with non-Lèvy superdiffusive random walks

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  • Fuentes, Emilio Aced
  • Santini, Simone

Abstract

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〉.

Suggested Citation

  • Fuentes, Emilio Aced & Santini, Simone, 2021. "Network navigation with non-Lèvy superdiffusive random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 580(C).
    • Handle: RePEc:eee:phsmap:v:580:y:2021:i:c:s0378437121004313
    DOI: 10.1016/j.physa.2021.126158
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    References listed on IDEAS

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    1. Lebensztayn, E. & Rodriguez, P.M., 2013. "A connection between a system of random walks and rumor transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5793-5800.
    2. de Guzzi Bagnato, Guilherme & Ronqui, José Ricardo Furlan & Travieso, Gonzalo, 2018. "Community detection in networks using self-avoiding random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 1046-1055.
    3. Marta C. González & César A. Hidalgo & Albert-László Barabási, 2009. "Understanding individual human mobility patterns," Nature, Nature, vol. 458(7235), pages 238-238, March.
    4. A. Tabrizi, Shayan & Shakery, Azadeh & Asadpour, Masoud & Abbasi, Maziar & Tavallaie, Mohammad Ali, 2013. "Personalized PageRank Clustering: A graph clustering algorithm based on random walks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(22), pages 5772-5785.
    5. Sen, Parongama, 2019. "Unusual scaling in a discrete quantum walk with random long range steps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 266-273.
    6. D. Brockmann & L. Hufnagel & T. Geisel, 2006. "The scaling laws of human travel," Nature, Nature, vol. 439(7075), pages 462-465, January.
    7. Xu, Xiao-Ke & Zhu, Jonathan J.H., 2016. "Flexible sampling large-scale social networks by self-adjustable random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 356-365.
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