I was wondering what the arrows actually mean. Turns out A->B means that A can be reduced to B (using a "polynomial-time many-one reduction"). So if we assume that B is NP-complete, A is too.

So it all boils down to showing that Circuit Satisfiability is NP-complete. I guess this graph shows the order in which the reductions were actually done for the first time. When I was at college, we reduced everthing to 3-SAT and directly proved that 3-SAT is NP-complete, I think.