ABSTRACT
This chapter emphasizes the properties of digraphs which set them apart from graphs. It explores by developing three different kinds of connectedness: strong, unilateral, and weak. The chapter presents the Directional Duality Principle, discusses matrices related to digraphs and the analogue of the Matrix Tree Theorem for graphs. A digraph is strongly connected, or strong, if every two points are mutually reachable; it is unilaterally connected, or unilateral, if for any two points at least one is reachable from the other; and it is weakly connected. The chapter notes that the trivial digraph, consisting of exactly one point, is strong since it does not contain two distinct points. It provides the state necessary and sufficient conditions for a digraph to satisfy each of the three kinds of connectedness. Corresponding to connected components of a graph, there are three different kinds of components of a digraph. The chapter concludes with a brief description of tournaments.
