The *traditional* approach of stCon shows that there is a edge between two vertices in a graph and this problem can be solved on a TM by a non deterministic algorithm like this:

$<G,u,v>, G = (V,E)$ is a graph with the nodes $V={1,2,…,m}$

```
x := u
repeat m-times:
if x == v:
accept
pick non-deterministic y from V
if (x,y) element of E:
x := y
otherwise reject
reject
```

If I want to check if there are two distinct edges to connect two vertices, I need to basically do the same but check if the paths that were found contain different vertices right? So how can one change this algorithm to accomplish that?