Databook says that Mihawk is the strongest swordsman in both name in actuality, he who has challenged all the strong swordsmen. Vista was literally happy to hear Mihawk knows his name. So please, stop.
Wow, what a genius to quote the magazine that isn't even written by Oda. A magazine that in the same sentence says that Shanks has the highest bounty, which was confirmed false. Apart from that, it doesn't say "equally fight" with the admirals. But that he is strong enough to fight them. Doesn't mean they can push him to his limits.