Discrete duality principle in different random graph models
Document typeMaster thesis
Rights accessOpen Access
For a given random graph, a connected component that contains a finite fraction of the entire graph's vertices is called giant. The study of these components started with the \ER model, where it has been proven that removing the (unique) giant component from a random graph is essentially equivalent to another random graph in the same model with different known parameters. This is called the discrete duality principle. In this report we aim at presenting this principle in its historical \ER settings, and then to present more recent generalisations made on random graphs with given degree sequences.