Is every pair of NP-Complete problems reduced in polynomial time?

As shown above, several NP-Complete problems are derived from GSAT (general satisfiability problem) by a polynomial-time reduction.

Then, my question is that is every pair of NP-Complete problems reduced in polynomial time? In other words, I think that the above graph should be represented as a complete graph by the definition of NP-Hard. Is it correct?

Yes, Let $$A,B$$ be two NP-complete problems. Then, by definition,
1. $$A,B\in NP$$
2. Every language $$L\in NP$$ can be reduced to them.
Hence, since $$B\in NP$$, then $$B\le_p A$$, and with a similar argument, $$A\le_p B$$.