Technische Universiteit Eindhoven, Stochastics W&I
Many real-world networks display a community structure. However, most random graph models do not contain many cycles, making them unfit for modeling networks with a community structure. We introduce a random graph model with a community structure, which we call the hierarchical configuration model. On the inter-community level, the graph is a configuration model, and on the intra-community level, every vertex replaced by a community: a small graph. Using this random graph model, we find that the community structure of real-world networks is an important determinant of how percolation processes such as virus spreading behave across a network.