So i just read about this theory that Mihawk might be the son of Rayleigh.
Basically it is this.
Mihawk is the worlds greatest swordsman.
Zoro is a top swordsman, and #2 in the Strawhat Crew
Rayleigh is also #2 on th PKs crew, and we all know Zoro is in many ways mirrored to Rayleigh.
Rayleigh may very well be a top swordsman.
Shanks seem very close to Mihawk. He might know him because he knows Rayleigh.
Mihawk as far as we know, have no connections to anyone we know of other than Shanks. He has no pirate crew, and he lives alone. Rayleigh also likes to live secluded. We know Oda like to connect everyone and everything.
Zoro who is #2, is trained by Mihawk. And if Zoro is mirrored after Rayleigh, then thats another connection.
Rayleight is also called the "Dark Knight", and Mihawk is a Dark Knight.
Mihawk is like a vampire. Guess what Vampires primary enemies are? Werewolves!!!! "Silver" bullets kills Werewolves.
The theory sounds like a mess when I type it out, but you get the jist.