Math Insight

Directed graph definition


A directed graph is graph, i.e., a set of objects (called vertices or nodes) that are connected together, where all the edges are directed from one vertex to another. A directed graph is sometimes called a digraph or a directed network. In contrast, a graph where the edges are bidirectional is called an undirected graph.

When drawing a directed graph, the edges are typically drawn as arrows indicating the direction, as illustrated in the following figure.

Small directed network with labeled nodes and edges

A directed graph with 10 vertices (or nodes) and 13 edges.

One can formally define a directed graph as $G= (\mathcal{N},\mathcal{E})$, consisting of the set $\mathcal{N}$ of nodes and the set $\mathcal{E}$ of edges, which are ordered pairs of elements of $\mathcal{N}$.