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 Z^d, 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.

By Philippe Deprez, Mario V. Wüthrich. n this article we provide an explicit algorithm to construct directed assortative configuration graphs based on a given bi-degree distribution and an arbitrary pre-specified assortativity.

This article provides a case study that analyzes national macroprudential insurance regulation in Switzerland. We consider an insurance market that is based on data from the Swiss private insurance industry. We stress this market with several scenarios related to financial and insurance risks, and we analyze the resulting risk capitals of the insurance companies. This stress-test analysis provides insights into the vulnerability of the Swiss private insurance sector to different risks and shocks.

The theory of random graphs goes back to the late 1950s when Paul Erd\H{o}s and Alfr\'ed R\'enyi introduced the Erd\H{o}s-R\'enyi random graph. Since then many models have been developed, and the study of random graph models has become popular for real-life network modelling such as social networks and financial networks. The aim of this overview is to review relevant random graph models for real-life network modelling. Therefore, we analyse their properties in terms of stylised facts of real-life networks.