Definition:Minimal Length Path

Definition
Let $G = \struct {V, E}$ be a simple graph.

Let $u, v \in V$ be vertices of $G$.

Let $W$ be the set of all open paths between $u$ and $v$.

An open path $p \in W$ is a minimal length path from $u$ to $v$ :


 * there exists no path $q$ beginning at $u$ and ending at $v$ such that the length of $q$ is (strictly) less than the length of $p$.