A Complex Graph Problem

A **weighted directed graph** consists of a set $V$ of **vertices** and a collection $E$ of **edges**. Each edge $e \in E$ is an ordered triple $e = (x, y, w)$ where $x \in V$ and $y \in V$ are vertices, called the **start** and **end** vertices of $e$, respectively, and $w$ is a number called the **weight** of $e$. A **walk** from vertex $s$ to vertex $t$ is an *alternating* sequence of vertic