A few things the Vivre Card Databook confirms:
Shanks was already a Yonko 12 years ago when he dueled Mihawk and met Luffy. This explains why Whitebeard praised their battles as legendary. This also means that Shanks became a Yonko without a devil fruit, because he was able to swim when he saved Luffy.
Mihawk is the “World’s Best” in name and actuality. There’s no unknown swordsman thats secretly stronger than him. This also suggests that Mihawk is atleast equal to Shanks.
Mihawk traveled the world alone fighting every strong swordsman he could find, until there was no one left. His last obstacle before becoming the World’s Strongest Swordsman was a Yonko-level swordsman with no Devil Fruit. After Shanks retired, there was no one left, so he got the title. He couldnt become a Yonko because he was alone, he had no territories or armies of crewmates.
Mihawk is waiting for someone stronger than Shanks to one day appear. The implications of this statement are pretty important. If he was weaker than Shanks, then someone on Shanks level would be more than enough for him. He wouldn’t look for someone stronger. If he was on his level, an idea that his duels with Yonko Shanks would support, then it would make sense he would want someone stronger.
I think this information pretty much confirms that Mihawk is Yonko level. It also heavily suggests that Mihawk = Shanks, and that Zoro will beat Mihawk when he surpasses Shanks. Thoughts?
*Theory by 4FunRegion