General theory for extended-range percolation on simple and multiplex networks

Fuente: arXiv
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Autori principali: Cirigliano, Lorenzo, Castellano, Claudio, Bianconi, Ginestra
Natura: Preprint
Pubblicazione: 2024
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author Cirigliano, Lorenzo
Castellano, Claudio
Bianconi, Ginestra
author_facet Cirigliano, Lorenzo
Castellano, Claudio
Bianconi, Ginestra
contents Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally tree-like. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram merges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte-Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.
format Preprint
id arxiv_https___arxiv_org_abs_2407_04585
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle General theory for extended-range percolation on simple and multiplex networks
Cirigliano, Lorenzo
Castellano, Claudio
Bianconi, Ginestra
Statistical Mechanics
Disordered Systems and Neural Networks
Extended-range percolation is a robust percolation process that has relevance for quantum communication problems. In extended-range percolation nodes can be trusted or untrusted. Untrusted facilitator nodes are untrusted nodes that can still allow communication between trusted nodes if they lie on a path of distance at most R between two trusted nodes. In extended-range percolation the extended-range giant component (ERGC) includes trusted nodes connected by paths of trusted and untrusted facilitator nodes. Here, based on a message passing algorithm, we develop a general theory of extended-range percolation, valid for arbitrary values of R as long as the networks are locally tree-like. This general framework allows us to investigate the properties of extended-range percolation on interdependent multiplex networks. While the extended-range nature makes multiplex networks more robust, interdependency makes them more fragile. From the interplay between these two effects a rich phase diagram merges including discontinuous phase transitions and reentrant phases. The theoretical predictions are in excellent agreement with extensive Monte-Carlo simulations. The proposed exactly solvable model constitutes a fundamental reference for the study of models defined through properties of extended-range paths.
title General theory for extended-range percolation on simple and multiplex networks
topic Statistical Mechanics
Disordered Systems and Neural Networks
url https://arxiv.org/abs/2407.04585