In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph, or set of nodes connected by edges, where the edges have a direction associated with them. In formal terms, a digraph is a pair (sometimes ) of:
- a set V, whose elements are called vertices or nodes,
- a set A of ordered pairs of vertices, called arcs, directed edges, or arrows (and sometimes simply edges with the corresponding set named E instead of A).
It differs from an ordinary or undirected graph, in that the latter is defined in terms of unordered pairs of vertices, which are usually called edges.
Sometimes a digraph is called a simple digraph to distinguish it from a directed multigraph, in which the arcs constitute a multiset, rather than a set, of ordered pairs of vertices. Also, in a simple digraph loops are disallowed. (A loop is an arc that pairs a vertex to itself.) On the other hand, some texts allow loops, multiple arcs, or both in a digraph.
Read more about Directed Graph: Basic Terminology, Indegree and Outdegree, Digraph Connectivity, Classes of Digraphs, See Also
Famous quotes containing the words directed and/or graph:
“Having a thirteen-year-old in the family is like having a general-admission ticket to the movies, radio and TV. You get to understand that the glittering new arts of our civilization are directed to the teen-agers, and by their suffrage they stand or fall.”
—Max Lerner (b. 1902)
“When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.”
—Marshall McLuhan (1911–1980)