The Relation Between Topological Ordering and Adjacency Matrix in Digraphs

In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, fi rst the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of adjacency matrix in acyclic digraphs are presented.