From Reachability Matrix to Hierarchical Matrix

The Hierarchical Reachability Matrix is constructed in order to partition the element set into levels.

Process

1. Two subsets of the element set are constructed for each element e_i:
   1. 1. The reachability set R_i which involves all of those elements that are reachable from element e_i
      2. An antecedent set A_i which involves all of those elements that reach element e_i.

In other words for each element e_i the set R_i can be determined as the set of elements whose columns have an entry of 1 in row i of the Reachability Matrix.