Query regarding the structure of Graph over All (known/unknown) NPC Problems?
The definition of NP-complete is that the problem is in NP and every problem in NP (including every other NP-complete problem) is reducible to that problem. So the graph you describe is not only strongly connected: it is a complete graph.
By the above, the distance between any two problems is&nbsp;1. But, even if you follow a longer path of $k$&nbsp;reductions, where the $i$th has polynomial blow-up&nbsp;$p_i$, the total blow-up for an input of size&nbsp;$n$ is $p_k(p_{k-1}(\cdots p_1(n)\cdots))$, which is still a polynomial.