Edie had a fling that was kept secret at the time with Dylan. She got over it fairly easily after the initial shock of finding out that Dylan had married someone else. Her relationship with the strongest emotional connection and length of time was with Bob Neuwirth, Dylan's right hand man. When Edie went home for Christmas and her Father had her committed, Neuwirth called and her Father bragged to him that he had drugged Edie, told her that she had a high fever and must go to the hospital, called the police and said that she was threatening homicide (to kill her sister and Mother), suicide, and running around naked, and then had a police car come and pick her up. Neuwirth told him that if he didn't have Edie on the phone within 24 hrs he would have his attorneys in L.A. get involved. Edie was released and got off the plane first class in New York, barefoot and smiling as if nothing bad had happened. (And personally, this is what I love about Edie, her ability to throw off the bad and smile in spite of all the painful things she had been through in her life is to me what makes her heroic.)

There is much more on her relationship with Neuwirth, but very little about Dylan, as neither one of them spoke of it, and my understanding was that it only existed for one month.
If you are interested in Edie, there is her last movie "Ciao! Manhattan" and two books on Edie. "Girl on Fire" is full of beautiful photos and quotes from people that knew Edie, and "Edie: An American Biography" by Jean Stein is also people quoting things about Edie, Warhol, and everyone that ever knew Edie who would contribute to the book. It goes all the way back to her family history of the Sedgwicks who were friends with the people who wrote the Declaration of Independence. Some people prefer "Edie: An American Biography" but to me, there is a great deal of reading about Warhol and his life,etc, basically reading about people other than Edie herself. But when you do come to the parts about Edie, they are raw and revealing. Girl on Fire has full page photos of Edie and is generally much more complimentary about her.