Random multi-hopper model
- We develop a mathematical model considering a random walker with long-range hops on arbitrary graphs. The random multi-hopper can jump to any node of the graph from an initial position, with a probability that decays as a function of the shortest-path distance between the two nodes in the graph. We consider here two decaying functions in the form of Laplace and Mellin transforms of the shortest-path distances. We prove that when the parameters of these transforms approach zero asymptotically, the hitting time in the multi-hopper approaches the minimum possible value for a normal random walker. We show by computational experiments that the multi-hopper explores a graph with clusters or skewed degree distributions more efficiently than a normal random walker. We provide computational evidences of the advantages of the random multi-hopper model with respect to the normal random walk by studying deterministic, random and real-world networks.
Author details: | Ernesto EstradaORCiD, Jean-Charles Delvenne, Naomichi HatanoORCiD, Jose L. Mateos, Ralf MetzlerORCiDGND, Alejandro P. Riascos, Michael T. Schaub |
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DOI: | https://doi.org/10.1093/comnet/cnx043 |
ISSN: | 2051-1310 |
ISSN: | 2051-1329 |
Title of parent work (English): | Journal of Complex Networks |
Subtitle (English): | super-fast random walks on graphs |
Publisher: | Oxford Univ. Press |
Place of publishing: | Oxford |
Publication type: | Article |
Language: | English |
Date of first publication: | 2018/10/03 |
Publication year: | 2018 |
Release date: | 2021/11/12 |
Volume: | 6 |
Issue: | 3 |
Number of pages: | 22 |
First page: | 382 |
Last Page: | 403 |
Funding institution: | the Marie Sklodowska-Curie grantEuropean Union (EU) [702410]; Concerted Research Action (ARC) programme - Federation Wallonia-Brussels [ARC 14/19-060]; DFGGerman Research Foundation (DFG) [ME 1535/6-1] |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
DDC classification: | 5 Naturwissenschaften und Mathematik / 53 Physik / 530 Physik |