structural:scholar_edition
Basic terminology

An arc (x, y) is considered to be directed from x to y; y is called the head and x is called the tail of the arc; y is said to be a direct successor of x and x is said to be a direct predecessor of y. If a path leads from x to y, then y is said to be a successor of x and reachable from x, and x is said to be a predecessor of y. The arc (y, x) is called the reversed arc of (x, y).

The adjacency matrix of a multidigraph with loops is the integer-valued matrix with rows and columns corresponding to the vertices, where a nondiagonal entry a is the number of arcs from vertex i to vertex j, and the diagonal entry a is the number of loops at vertex i. The adjacency matrix of a directed graph is a logical matrix, and isunique up to permutation of rows and columns.

Another matrix representation for a directed graph is its incidence matrix.

See direction for more definitions.