CHARLOTTESVILLE, Va. (AP) — Remains found nearly a week ago in a rural area of Virginia are those of a university student who disappeared last month, authorities said Friday, ending a search by thousands that took weeks and left the campus and community on edge.

University of Virginia sophomore Hannah Graham, 18, disappeared Sept. 13 after a night out with friends. The remains were found Oct. 18 about 12 miles from the Charlottesville campus, in a heavily wooded area of Albemarle County that is home to rolling hills and horse farms.

The state Medical Examiner's office confirmed that the remains were Graham's, the Albermarle County Police Department said in a statement.

The man Graham was last seen with, 32-year-old Jesse Leroy Matthew Jr., has been charged with abduction with intent to defile Graham. His attorney, Jim Camblos, said in a voicemail greeting that he is not answering questions about the case.

The remains were discovered roughly 6 miles from where the body of 20-year-old Virginia Tech student Morgan Harrington was found after she vanished in 2009. Police have said forensic evidence connects Matthew to Harrington's killing, which in turn is linked by DNA to a 2005 sexual assault in northern Virginia. Matthew has been charged in the 2005 case.

"When we started this journey together we all hoped for a happier ending. Sadly that was not to be," Graham's parents, John and Sue Graham, said in a statement provided by the police department. "We are devastated by the loss of our beautiful daughter. ... Although we have lost our precious Hannah, the light she radiated can never be extinguished."

Graham's parents also thanked those involved with the investigation and search efforts — singling out Charlottesville Police Chief Tim Longo for his "tenacity and determination — as well as those who have sent messages of support. They said they don't intend to make further statements or comment on the ongoing criminal investigation.

Longo, who became the public face of the investigation through emotional pleas for the public's help finding Graham, did not immediately respond to a telephone call seeking comment.

Albemarle County Commonwealth's Attorney Denise Lunsford said in a statement that the focus of the investigation now is to determine "what charges will be brought and the appropriate time to make those charges."

Graham's disappearance prompted many University of Virginia students to begin walking in pairs or groups at night. Also, the university expanded a ride service for its students.

"For Hannah's young life to end so tragically, and for her destiny of promise to be left unfulfilled, is an affront to the sanctity of life and to the natural order of human events," university President Teresa A. Sullivan said in a statement Friday evening. "This is a sorrowful day in the life of the university, and our entire community is grieving with the Graham family."

Carli Sapir, a fourth-year environmental engineering student, lived only a half-block away from Hannah's residence at U.Va.

"This conclusion wasn't the conclusion we were hoping for," she said. "Of course we all had a hope that even after all this time that they would find her living. It's pretty devastating."

Sapir, from Long Valley, New Jersey, said her apartment is only a 30-second walk from Hannah's on 14th and 15th streets in Charlottesville.

"Even though I didn't know her personally, it's crazy that something so bad could happen to one of our fellow students," she said.

Graham met friends at a restaurant for dinner Sept. 12 before stopping by two off-campus parties. She left the second party alone and eventually texted a friend saying she was lost, authorities said.

In surveillance video, she can be seen walking unsteadily and even running at times, past a pub and a service station and then onto a seven-block strip of bars, restaurants and shops.

Matthew was an operating room technician at the university's hospital. He was also a former college football lineman and sometimes cab driver.

Friends have said they were shocked the "gentle giant" — he's 6-foot-2 and weighs 270 pounds — could be suspected of such violence.

Matthew was co-captain of his high school football team and enrolled in psychology at evangelist Jerry Falwell's Liberty University, where he played on the defensive line for the Flames.

His college career took a sharp wrong turn in his junior year, when a fellow student accused Matthew of raping her. Matthew withdrew from Liberty on Oct. 17, 2002 — hours after a reported sexual assault behind the university's sports arena. Prosecutors said the case was dropped when the woman declined to press charges.

Matthew returned to school in January 2003, enrolling at Christopher Newport University in southeast Virginia. He joined their football team that August, but on Sept. 7, 2003, a fellow student accused him of sexual assault on the Newport News campus. Five days after the attack, Matthew dropped off the team roster; a month later, he was gone.

University spokesman Bruce Bronstein said the matter was thoroughly investigated and the victim decided not to press charges.

The victim in the 2005 rape in the Washington, D.C., suburbs is cooperating with authorities, Fairfax County Commonwealth's Attorney Ray Morrogh has said. According to police, a 26-year-old woman was walking home from the grocery store about 10 p.m. on a Saturday night when she was grabbed from behind, dragged into a wooded area behind some townhomes, and sexually assaulted. The man fled the area when he was startled by a passerby.

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O'Dell reported from Richmond, Va. Associated Press Writer Michael Felberbaum in Richmond contributed to this report.