# Directed Graph

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A directed graph is a graph whose graph edges are all directed graph edges.

## References

### 2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/directed_graph Retrieved:2013-12-8.
• 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 [math]G=(V,A)[/math] (sometimes [math]G=(V,E)[/math]) of: [1]
• 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.

1. . , Section 1.10. , Section 10.