The actress still remains close with her dad who raised her after her parents' divorce

Although Lauren Graham is best known as half of the fast-talking mother-daughter duo from Gilmore Girls, in real life, the actress, 49, has a similarly close relationship with her father, Lawrence Graham, who raised her after her parents divorced when she was 5.

“Like any kid, I just thought what I had was normal,” she says of her childhood in Virginia. “Divorce was less common, and to have my dad be the single parent was unusual, but we had a lot of fun.”

In her new book of personal essays, Talking as Fast as I Can: From Gilmore Girls to Gilmore Girls (and Everything in Between), Graham writes about her close relationship with her dad and tells PEOPLE, “I thought I kind of had it best. My dad has a very mellow way about him and I was a self-starter as a kid. I liked a certain amount of being on my own. It just worked great for me.”

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Credit: Courtesy Lauren Graham
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Graham, who is reprising her role as Lorelai Gilmore for a reboot of Gilmore Girls: A Year in the Life, says her dad would often take her to wherever he was going, and she has fond memories of going with him to the theater, museums and restaurants.

“I wasn’t like, ‘poor us, we have to go to another restaurant.’ We had a great time!”

Gilmore Girls: A Year in the Life premieres Nov. 25 on Netflix.