Inhomogeneous Long-Range Percolation for Real-Life Network Modeling
The study of random graphs has become very popular for real-life network modeling, such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice Zd, d ≥ 1, is a particular attractive example of a random graph model because it fulfills...
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| Format: | Article |
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MDPI AG
2015-01-01
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| Series: | Risks |
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| Online Access: | http://www.mdpi.com/2227-9091/3/1/1 |
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| author | Philippe Deprez Rajat Subhra Hazra Mario V. Wüthrich |
| author_facet | Philippe Deprez Rajat Subhra Hazra Mario V. Wüthrich |
| author_sort | Philippe Deprez |
| collection | DOAJ |
| description | The study of random graphs has become very popular for real-life network modeling, such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice Zd, d ≥ 1, is a particular attractive example of a random graph model because it fulfills several stylized facts of real-life networks. For this model, various geometric properties, such as the percolation behavior, the degree distribution and graph distances, have been analyzed. In the present paper, we complement the picture of graph distances and we prove continuity of the percolation probability in the phase transition point. We also provide an illustration of the model connected to financial networks. |
| first_indexed | 2024-04-12T00:48:21Z |
| format | Article |
| id | doaj.art-8e3094c1a0c84e41a3099ca645475ac0 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-04-12T00:48:21Z |
| publishDate | 2015-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-8e3094c1a0c84e41a3099ca645475ac02022-12-22T03:54:49ZengMDPI AGRisks2227-90912015-01-013112310.3390/risks3010001risks3010001Inhomogeneous Long-Range Percolation for Real-Life Network ModelingPhilippe Deprez0Rajat Subhra Hazra1Mario V. Wüthrich2RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, SwitzerlandIndian Statistical Institute, Theoretical Statistics and Mathematics Unit, Kolkata 700 108, IndiaRiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, SwitzerlandThe study of random graphs has become very popular for real-life network modeling, such as social networks or financial networks. Inhomogeneous long-range percolation (or scale-free percolation) on the lattice Zd, d ≥ 1, is a particular attractive example of a random graph model because it fulfills several stylized facts of real-life networks. For this model, various geometric properties, such as the percolation behavior, the degree distribution and graph distances, have been analyzed. In the present paper, we complement the picture of graph distances and we prove continuity of the percolation probability in the phase transition point. We also provide an illustration of the model connected to financial networks.http://www.mdpi.com/2227-9091/3/1/1network modelingstylized facts of real-life networkssmall-world effectlong-range percolationscale-free percolationgraph distancephase transitioncontinuity of percolation probabilityinhomogeneous long-range percolationinfinite connected component |
| spellingShingle | Philippe Deprez Rajat Subhra Hazra Mario V. Wüthrich Inhomogeneous Long-Range Percolation for Real-Life Network Modeling Risks network modeling stylized facts of real-life networks small-world effect long-range percolation scale-free percolation graph distance phase transition continuity of percolation probability inhomogeneous long-range percolation infinite connected component |
| title | Inhomogeneous Long-Range Percolation for Real-Life Network Modeling |
| title_full | Inhomogeneous Long-Range Percolation for Real-Life Network Modeling |
| title_fullStr | Inhomogeneous Long-Range Percolation for Real-Life Network Modeling |
| title_full_unstemmed | Inhomogeneous Long-Range Percolation for Real-Life Network Modeling |
| title_short | Inhomogeneous Long-Range Percolation for Real-Life Network Modeling |
| title_sort | inhomogeneous long range percolation for real life network modeling |
| topic | network modeling stylized facts of real-life networks small-world effect long-range percolation scale-free percolation graph distance phase transition continuity of percolation probability inhomogeneous long-range percolation infinite connected component |
| url | http://www.mdpi.com/2227-9091/3/1/1 |
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