In a constraint graph, a new vertex $\backslash ($ v$\_\{0\}\backslash )$ is often added to simplify the problem of finding shortest paths from a single source to all other vertices. This new vertex $\backslash ($ v$\_\{0\}\backslash )$ is typically connected to every other vertex $\backslash ($ v$\_\{$i$\}\backslash )$ with an edge weight of $0,$ ensuring that each vertex is reachable without introducing any additional costs. Can any shortest$-$path weight from the new vertex $\backslash ($ v$\_\{0\}\backslash )$ in a constraint graph be positive? Explain.