I'm coming from this thread: Prove that a strongly connected digraph has an irreducible adjacency matrix? (can't ask in the comments there unfortunately) and there's one statement I can't prove:
"for all $i\in V_1$ and $j\in V_2$. Since $V$ is strongly connected, there exists a path $i_1i_2\dots i_n$ where $i_1$ is some point in $V_1$ and $i_2$ is some point in $V_2$."
how do I know there's always such a path?