Self-attracting walk on heterogeneous networks

Kanghun Kim, Jaegu Kyoung, and D.-S. Lee
Phys. Rev. E 93, 052310 – Published 25 May 2016

Abstract

Understanding human mobility in cyberspace becomes increasingly important in this information era. While human mobility, memory-dependent and subdiffusive, is well understood in Euclidean space, it remains elusive in random heterogeneous networks like the World Wide Web. Here we study the diffusion characteristics of self-attracting walks, in which a walker is more likely to move to the locations visited previously than to unvisited ones, on scale-free networks. Under strong attraction, the number of distinct visited nodes grows linearly in time with larger coefficients in more heterogeneous networks. More interestingly, crossovers to sublinear growths occur in strongly heterogeneous networks. To understand these phenomena, we investigate the characteristic volumes and topology of the cluster of visited nodes and find that the reinforced attraction to hubs results in expediting exploration first but delaying later, as characterized by the scaling exponents that we derive. Our findings and analysis method can be useful for understanding various diffusion processes mediated by human.

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  • Received 12 December 2015
  • Revised 14 April 2016

DOI:https://doi.org/10.1103/PhysRevE.93.052310

©2016 American Physical Society

Physics Subject Headings (PhySH)

Networks

Authors & Affiliations

Kanghun Kim, Jaegu Kyoung, and D.-S. Lee*

  • Department of Physics, Inha University, Incheon 402-751, Korea

  • *deoksun.lee@inha.ac.kr

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Issue

Vol. 93, Iss. 5 — May 2016

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