\begin{definition}[Definition:In-Degree]
Let $G = \struct {V, E}$ be a digraph.
Let $v \in V$ be a vertex of $G$.
The '''in-degree of $v$ in $G$''' is the number of arcs which are incident to $v$. 
It is denoted $\map {\operatorname {indeg}_G} v$, or just $\map {\operatorname {indeg} } v$ if it is clear from the context which digraph is being referred to.
\end{definition}