  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.
  Furthermore, we determine the conditions under which a giant percolation
cluster exists, and find its size.
