General theory for extended-range percolation on simple and multiplex networks
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914966300262400 |
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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 |