Inhomogeneous long-range percolation for real-life network modeling

• Published in: Risks (Basel) Vol. 3; no. 1; pp. 1 - 23
• Main Authors: Deprez, Philippe, Hazra, Rajat Subhra, Wüthrich, Mario V
• Format: Journal Article
• Language: English
• Published: Basel MDPI 01-03-2015; MDPI AG
• Subjects: Analysis; continuity of percolation probability; graph distance; Graph theory; infinite connected component; inhomogeneous long-range percolation; long-range percolation; network modeling; Network topologies; phase transition; scale-free percolation; small-world effect; Social networks; Studies; stylized facts of real-life networks
• ISSN: 2227-9091; 2227-9091
• DOI: 10.3390/risks3010001

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 Ï 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.