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Risks 2015, 3(1), 1-23; doi:10.3390/risks3010001

Inhomogeneous Long-Range Percolation for Real-Life Network Modeling

1
RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
2
Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, Kolkata 700 108, India
3
Swiss Finance Institute SFI Professor, 8006 Zurich, Switzerland
*
Author to whom correspondence should be addressed.
Academic Editor: Michael R. Powers
Received: 26 September 2014 / Accepted: 22 December 2014 / Published: 6 January 2015
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Abstract

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. View Full-Text
Keywords: 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 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
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Deprez, P.; Hazra, R.S.; Wüthrich, M.V. Inhomogeneous Long-Range Percolation for Real-Life Network Modeling. Risks 2015, 3, 1-23.

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