Directed graphs and their adjacency matrices: Misconceptions and more efficient methods

Commonly useful properties of directed graphs and their adjacency matrices are briefly reviewed. Some misconceptions presented in earlier papers, relating to indicators in the adjacency matrix of the occurrence of multiple laps of cycles and of compound cycles composed of several shorter cycles, are corrected. Shortcomings of an earlier method for finding cycles are discussed and a simple, improved method for finding all cycles, or all paths between two nodes of interest, is presented. Shortcomings of an earlier method of suppressing unwanted cycle effects are discussed and a simple, improved method for this is presented. Results obtained from this method are compared with those for the same case where cycle suppression is not used.