Let \(D=(V,E,\alpha,\omega)\) be a digraph, \(v\in V\) be a vertex of \(D\).
The number \(d_D^+(v)\) of edges outgoing from \(v\), i.e. the number of elements of the set \(\delta_D^+(v):=\{e\in E: \alpha(e)=v\}\), is called the outer degree of \(v\), formally \(d_D^+(v):=|\delta_D^+(v)|\).
The number \(d_D^-(v)\) of edges incoming to \(v\), i.e. the number of elements of the set \(\delta_D^-(v):=\{e\in E: \omega(e)=v\}\) is called the inner degree of \(v\), formally \(d_D^-(v):=|\delta_D^-(v)|\).
The number \(d_D(v):=d_D^+(v)+d_D^-(v)\) is called the degree of \(v\).
Note: In the above definitions, the index \(D\) can be omitted in the notation, if it is clear from the context, which digraph \(D\) is concerned.
The values of the degrees of vertices in the above graph are:
| Vertex \(v\) | Degree \(d(v)\) | Inner Degree \(d^-(v)\) | Outer Degree \(d^+(v)\) |
|---|---|---|---|
| \(a\) | \(5\) | \(2\) | \(3\) |
| \(b\) | \(6\) | \(4\) | \(2\) |
| \(c\) | \(4\) | \(1\) | \(3\) |
| \(d\) | \(3\) | \(1\) | \(2\) |
| \(e\) | \(4\) | \(3\) | \(1\) |
| \(f\) | \(0\) | \(0\) | \(0\) |
