The versatile Graf used her powerful forehand and exceptional footwork to win seven Wimbledon titles, six French Opens, five U.S. Opens, and four Australian titles.
She's the only singles player male or female to win the calendar year Golden Grand Slam. This year marks the 25th anniversary of her winning all four Grand Slam titles and the gold medal at the 1988 Seoul Olympics.
In her final season in 1999, Graf beat a 17-year-old Williams in Sydney and lost to her at Indian Wells. Those meetings were memorable.
"You can feel a strong energy and determination," Graf said. "That can be definitely intimidating playing against her. You know there's a force on the court. Obviously, she tries to take points over, then you feel pressure to be aggressive.
"Even in her young age, she and her sister (Venus), they just had a really strong presence on the court."
On Friday, Williams was guaranteed to finish the year with the No. 1 ranking for the third time in her career. Graf achieved that feat a record eight times.
She won 107 singles titles, finishing third on the WTA list after Navratilova (167) and Evert (157).
Graf captured an astounding seven of eight majors from 1988-89 in her prime. If Serena wins two majors each in the next three years, she would pass Graf by the end of the 2016 season.
"We'll see how mentally and physically she's able to preserve herself over the next few years," Graf said. "I don't think anybody's ever played that far, that kind of tennis, at her age. I'll be curious to follow her."
Graf noticed the improved play of Williams this season.
"I thought she really put it together well in her matches this year determined, focused," Graf said. "She's seemed to have found an inner calm on the court."
These days, the 44-year-old Graf and husband Andre Agassi are busy raising 11-year-old Jaden and 9-year old Jaz, who enjoy baseball and dance.
"They're really active, I guess they've caught that from their parents," she said, laughing. "Jaden has been playing baseball for about five years, he plays club ball, loves it. He's got a really intense schedule. When I look back at my tournaments at that age, he surpasses that easily.
"Jaz, the last three years, she's really loving dance, hip-hop. It's been fun seeing her branch out into something that might not be as natural for her. But she's coming out of her shell and really enjoying it."
Instead of tennis, Graf now relishes lower-impact biking, Pilates and yoga.
"For me, working out is essential," she said. "It's something, not only physically I need. I need it for my state of mind. It helps me to take some time for myself and organize my thoughts, and it gives me energy again."
Graf attended a Longines "Women Who Make A Difference" event in New York on Thursday night and promoted her foundation "Children for Tomorrow," which works with youth traumatized by war.
Agassi's College Preparatory Academy, which began in Las Vegas, has expanded to 25 charter schools nationwide, including another school in Detroit and two schools opening in Florida, she said.
"It's really personal and really important to us, and we share that intimately," Graf said before flying back to their home in Nevada. "It's the future of the country. It's giving kids a chance, with education, to make their own choices later in life.
"It's pretty moving when you see some of the responses of the parents."
