In this manner D partitions the edges that exist in G. The primary assumption in the hierarchical random graph model is that edges in G exist independently, but with a probability that is not identically distributed.
the probability that an edge {v i , v j } exists in G is given by a parameter θ k associated with D k , the lowest common ancestor of v i and v j in D. In this manner, the topological structure D and the vector of probabilities θ define the HRG given by H(D, θ) (Clauset et al., 2008).