Identifying Loops by Powers of the Adjacency Matrix
Identifying Loops by Powers of the Adjacency Matrix
The Adjacency matrix is a binary DSM where an empty cell is replaced with a
"zero" and a non-empty cell is replaced by "one".
Raising the DSM to the n-th power shows which element can be reached from
itself in n steps by observing a non-zero entry for that task along the diagonal of the
matrix. For example squaring the DSM (below) shows that tasks A and C are involved in a
two-step loop. [Note that in the resultant square matrix, cells with a value of
greater than one were replaced by a value of one].
Similarly, cubing the DSM, as shown below, shows that tasks B, D and E are
involved in a three-step loop. The higher powers of the DSM reveal no other loops in the
system.
