Hierarchical Configuration Model

Understand

We introduce a class of random graphs 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 in the configuration model is replaced by a community: i.e., a small graph.
• These communities may have any shape, as long as they are connected.
• For these hierarchical graphs, we find the size of the largest component, the degree distribution and the clustering coefficient.