Networks, Random Graphs and Percolation

preprint2014arXivOpen access

Abstract

The theory of random graphs goes back to the late 1950s when Paul Erdős and Alfréd Rényi introduced the Erdős-Rényi 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.

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