Graph maximal loop

The maximal loops in the graph can be found from the reachability matrix by finding those sets of vertices that satisfy the following conditions (1) r j = rfi = 1, where i and j take on all possible combinations of the vertex numbers in the set (2) no other vertices, not included in the set, satisfy condition (1). The first condition requires that each vertex in the set is reachable by some path from every other vertex in the set. The second condition requires that there is no path from a vertex in the set to a vertex outside the set... 

The maximal common subgraph of these two S-graphs does not contain an edge or loop, it contains only one vertex. The reaction graph is... 

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