The revelations about her mixed academic record add to the portrait of a principal figure in the Petraeus scandal who has refused to respond to multiple Globe requests for comment and hasn’t spoken publicly since disclosure of her relationship with Petraeus and his resignation as CIA chief.

Broadwell left Harvard with a lesser diploma in 2008, a master of public administration, after one additional semester.

She enrolled later that year as a PhD student in the war studies department of King’s College London, where her military leadership research focused largely on Petraeus, according to Broadwell’s profile on the school website. But four years on, Broadwell remains far from earning her degree, according to the department chairman, and her relationship with the subject of her research could jeopardize her progress toward a doctorate.

“We have a very stringent ethical review process,” said Mervyn Frost, head of the war studies department. “We found nothing wrong with her original proposal, but in light of what’s happened now, I suspect we’ll revisit that process.”

One of Broadwell’s former professors at Harvard described her as a self-promoter who would routinely show up at office hours.

“It was very much, ‘I’m here and you’re going to know I’m here,’ ” said the professor, who did not want to be identified because of the sensitivity of ongoing investigations. “She was not someone you would think of as a critical thinker. I don’t remember anything about her as a student. I remember her as a personality.”

The professor said when Petraeus chose Broadwell to write his biography, there was shock among the national security faculty at Harvard because “she just didn’t have the background — the academic background, the national security background, or the writing background.”

A second Harvard faculty member who knows Broadwell and Petraeus had similar misgivings.

At one point, Broadwell said she was leaving the doctorate track because she was over­extended and didn’t have time to complete the coursework, recounted the professor, who was not authorized to speak to the press.

Broadwell later complained that the writing project on Petraeus was not going well.

“She was a lot of talk but not a lot of follow-through,” said the second professor, who described Broadwell’s struggle to deliver on the biography as “deeply embarrassing” to the Kennedy School. “That is why she brought on a co-author,” Vernon Loeb, an editor at the Washington Post.

Nonetheless, Harvard embraced Broadwell as a distinguished alumna after “All In: The Education of General David Petraeus” became a New York Times bestseller this year. On Sept. 10, the Kennedy School included Broadwell on an alumni panel of accomplished public servants and the next day hosted a forum at which she discussed her book.

Broadwell, 40, says on her resume on the professional networking website LinkedIn that she obtained two master of arts degrees from the University of Denver, one in international security and one in international negotiations, before coming to Cambridge in September 2005. In fact, she was awarded only one degree, in international security in 2006, according to the university registrar.

Broadwell enrolled in Harvard’s public policy PhD program one month after she completed her studies in Denver. It was during her second semester, in the spring of 2006, that Broadwell met Petraeus for the first time, when he lectured at the Kennedy School about counterinsurgency in Iraq.

Broadwell was among a group of students who joined Petraeus for dinner after the event, and she kept in touch with him.

But Broadwell did not fulfill the demanding requirements of the public policy program that facilitated her meeting Petraeus. As a doctoral student, Broadwell was required to carry a full course load — four classes per semester. She also had to complete a research seminar, pass a series of exams, and submit and defend a dissertation, which typically required two or three years of research and writing.