Inhomogeneous Long-Range Percolation for Real-Life Network Modeling

Risks

Philippe Deprez²  Rajat Subhra Hazra¹  Mario V. Wüthrich² 

[1] Indian Statistical Institute, Theoretical Statistics and Mathematics Unit, Kolkata 700 108, India; E-Mail:;RiskLab, Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

关键词: 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;   

DOI  :  10.3390/risks3010001

来源: mdpi

【 摘 要 】

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 , 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.

【 授权许可】

CC BY   
© 2015 by the authors; licensee MDPI, Basel, Switzerland.