Networks, Random Graphs and Percolation

TL;DR

This paper reviews various random graph models used for real-life network modeling, analyzing their properties in relation to the typical features observed in social and financial networks.

Contribution

It provides a comprehensive overview of random graph models and their relevance to modeling real-world networks, highlighting their key properties and applications.

Findings

Random graph models capture key features of real networks

Different models suit different types of networks

Percolation theory explains network robustness

Abstract

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.