Percolation in fractal spatial networks with long-range interactions

Guy Amit; Dana Ben Porath; Sergey V. Buldyrev; Amir Bashan

doi:10.1103/PhysRevResearch.5.023129

Percolation in fractal spatial networks with long-range interactions

Guy Amit, Dana Ben Porath, Sergey V. Buldyrev, Amir Bashan

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We study the emergence of a giant component in a spatial network where the nodes form a fractal set, and the interaction between the nodes has a long-range power-law behavior. The nodes are positioned in the metric space using a Lèvy flight procedure, with an associated scale-invariant step probability density function, that is then followed by a process of connecting each pair of nodes with a probability that depends on the distance between them. Since the nodes are positioned sequentially, we are able to calculate the probability for an edge between any two nodes in terms of their indexes and to map the model to the problem of percolation in a one-dimensional lattice with long-range interactions. This allows the identification of the conditions for which a percolation transition is possible. The system is characterized by two control parameters which determine the fractal dimension of the nodes and the power law decrease of the probability of a bond with the distance between the nodes. The competition between these two parameters forms an intricate phase diagram, which describes when the system has a stable giant component, and when percolation transitions occur. Understanding the structure of this class of spatial networks is important when analyzing real systems, which are frequently heterogeneous and include long-range interactions.

Original language	English
Article number	023129
Journal	Physical Review Research
Volume	5
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevResearch.5.023129
State	Published - Apr 2023

Bibliographical note

Publisher Copyright:
© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Funding

We thank Shlomo Havlin, Eli Barkai, Stanislav Burov, and Stephane Plaszczynski for fruitful discussions and helpful suggestions. This work was supported by the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel (Grant No. 2020255). S.V.B. acknowledges the support of this research by DTRA (Grant No. HDTRA-1-19-1-0016) and the Dr. Bernard W Gamson Computational Science Center at Yeshiva College. A.B. thanks the Israel Science Foundation (Grant No. 1258/21), and the German-Israeli Foundation for Scientific Research and Development.

Funders	Funder number
Yeshiva University
German-Israeli Foundation for Scientific Research and Development
United States-Israel Binational Science Foundation	2020255, HDTRA-1-19-1-0016
Israel Science Foundation	1258/21

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10.1103/PhysRevResearch.5.023129

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Percolation in fractal spatial networks with long-range interactions

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