How do i make sure i get the correct Bellman Ford path?
From Wikipedia:

The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.

What is a shortest path? According to Wikipedia:

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

Wikipedia isn't always a reliable source, but in this case the definitions are spot on. Suppose that $G=(V,E,w)$ is a weighted undirected graph. A path between two vertices $x,y \in V$ is a list
$$ v_0 = x, v_1, \ldots, v_\ell = y $$
such that $(v_i,v_{i+1}) \in E$ for all $i &lt; \ell$ (possibly $\ell = 0$). The weight of the path is
$$ \sum_{i=0}^{\ell-1} w(v_i,v_{i+1}). $$
A shortest path between $x$ and $y$ is a path with minimum weight.
The Bellman–Ford algorithm finds the lengths of all shortest paths from a given vertex $x$ to all other vertices. It also generates auxiliary information which makes it possible to find the corresponding shortest paths.