William is survived by his wife Sally Lasker Graham and two children, Alice Graham and Edward Graham.
He is also survived by his two brothers, Donald Graham and Stephen Graham.
His death came six days after the film's premiere in Washington DC.
Graham was a prominent lawyer at the Williams & Connolly firm in Washington DC in the 1970s before he moved to Los Angeles.
Katharine, who was Meyer's daughter, oversaw the paper through some of its most important stories, including the Watergate scandal.
The recently released film recounts the behind-the-scenes story of the 1971 publication of the Pentagon Papers, which exposed the lies behind US involvement in the Vietnam War.
Graham, a 69-year-old lawyer, was found dead from a self-inflicted gunshot wound last Wednesday, according to an obituary published in the Post.
His father Phil, who was publisher of the newspaper for 17 years, killed himself back in 1963.
The Israeli military said it targeted air defense batteries and army bases as well as Iranian positions in a day of dramatic cross-border confrontations as the threat of a wider regional conflict loomed.
Israel said it launched the “large scale attack” after one of its F-16 fighter jets crashed under Syrian anti-aircraft fire.
Kim Jong Un’s smiling younger sister has surprised South Koreans with her low-key approach during her three-day Olympic-related visit as her brother’s special envoy.
South Korean broadcasters have drawn a parallel between her visit and that of President Trump’s daughter, who will attend the Closing Ceremonies.
Graham then devoted himself to philanthropic activities, many of which remained anonymous.