Nothing. Literally nothing.
That said, they do share some connective tissue. The back story: Last year, Gosling was photographed wearing a T-shirt that featured an image of Culkin from his "Home Alone" Kevin McCallister days.
A year later, Culkin made headlines for himself (and his weird Velvet Underground tribute band) by making a T-shirt that featured a photo of the paparazzi shot of Gosling wearing the Culkin T-shirt.
Are you still with me? If so, that's impressive. Now the Patriots connection. In reference to this seminal meta moment in American popular culture, Edelman made up a T-shirt that features a photo of a partying Gronkowski:
Julian Edelman (@Edelman11) May 19, 2014
Gronk, who almost certainly wasn't aware of the Culkin-Gosling back story and really is just about the good times, returned serve with a T-shirt of Edelman wearing the Gronk shirt.
Rob Gronkowski (@RobGronkowski) May 20, 2014
You can't possibly still be here. You are? Awesome.
Obviously, the biggest takeaway here is that members of the New England Patriots are having light-hearted fun in a public setting. They must be stopped so as to preserve tranquility along Patriot Way.