Graphical neighbours

Let $Γ$ be a general graph. The out-neighbours of a vertex $𝑣 \in V (Γ)$ is the set of all vertices reachable from $𝑣$ by a single arc graph

Γ + (𝑣) = {𝑤 \in 𝑉 : 𝑣 \to 𝑤}

and in-neighbours are defined analogously

Γ - (𝑣) = {𝑤 \in 𝑉 : 𝑤 \to 𝑣}

the cardinality of these being referred to as the out-degree and in-degree respectively.

If $Γ$ is a graph, the out-neighbours and in-neighbours coïncide and are denoted $Γ (𝑣)$ .
If $Γ$ is a multidigraph, these are multisets.