The concept of structure has become a central concern in the study of human perception, learning, memory, and recall. The purpose of this paper is to present a method for analyzing structure--the theory of directed graphs--and to review research on teaching that has employed this method to investigate input structure, memory structure, or both. To this end, the paper is divided into two parts. The first part presents fundamental concepts of the theory of directed graphs--digraphs: the axiom system, types of digraphs, adjacency, reachability, connectedness, distance, and vulnerability. In the second part, research is reviewed in which content structure, cognitive structure, and the correspondence between these structures are examined with implications for the teaching-learning process. Throughout this review, implications for further research on teaching using digraphs are set forth. (Author/RT)