Who is the most-connected (in the "six degrees" sense) seiyuu?
I don't know the specific answer for "most connected" seiyuu, but many companies did some ranking for seiyuu.

Oricon (Japanese) has a user-vote based ranking. Most known seiyuu is Nobuyo Oyama (e.g. Doraemon) and Masako Nozawa (e.g. Goku from Dragon Ball).

AppBank (Japanese) also has a ranking based on votes from other seiyuu. Top 3 is Koichi Yamadera, Masako Nozawa and Keiji Fujiwara. I think Yamadera is selected because there are lots of seiyuu worked with him.

I want to put my 2 cents to Koichi Yamadera because he has long career and variety of anime.