Here is a simple example:
In[1]:= TransitiveClosureGraph[{1->2, 2->3, 3->1}]//AdjacencyMatrix//MatrixForm
Out[1]//MatrixForm= 0 1 1
1 0 1
1 1 0
This produces the graph with the adjacency matrix of {{0,1,1},{1,0,1},{1,1,0}}, but I expected the diagonal elements to be 1 as well, i.e. a loop for each vertex. At least for a binary relation that would be the case, so I don't understand why the transitive closure for a graph is ignoring the loops. By the definition of transitive closure on MathWorld definition it is a graph which contains an edge {u,v} whenever there is a directed path from u to v. Well, in our case there is a directed path from 1 to 1, namely: 1->2, 2->3, 3->1. And likewise for the nodes 2 and 3. What am I missing here? Thank you.
