Story highlights Authorities looking for Graham found the remains last Saturday on an abandoned property

The remains are those of University of Virginia student Hannah Graham

"We all hoped for a happier ending," her parents say

Human remains discovered last weekend in Albemarle County, Virginia, belong to University of Virginia student Hannah Graham, authorities said Friday.

Graham, 18, went missing before dawn on September 13 after being last spotted on several surveillance cameras in Charlottesville's Downtown Mall area.

Authorities looking Graham found the remains last Saturday on an abandoned property eight miles from where the sophomore was last seen.

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Graham's parents, John and Sue, acknowledged the confirmation of the remains' identity, announced by the Virginia Medical Examiner's Office and the Albemarle County Police Department.

"When we started this journey together we all hoped for a happier ending," the couple said in a statement. "Sadly that was not to be, but due to the tenacity and determination of (Charlottesville Police Chief Timothy) Longo, Hannah is coming home to us and we will be eternally grateful to him for this.

"We are devastated by the loss of our beautiful daughter," the parents added.

Authorities are continuing their investigation, in which an abduction charge has been filed against one man.

"The focus of the investigation now is to determine what charges will be brought and the appropriate time to make those charges," according to a statement from the office of Albemarle County Commonweath's Attorney Denise Y. Lunsford.

Her office declined to comment further.

County police said they were moving "forward with the death investigation."

"Our focus is on the investigation and therefore, we will not be answering questions regarding the case or investigation. We do ask that people continue to call in with tips or information," a county police statement said.

The downtown Charlottesville camera footage showed Graham leaving the Tempo Bar at around 2 a.m. on September 13, as well as a man -- later identified by authorities as Jesse Matthew, 32 -- following her.

On September 24, Matthew was taken into custody while camping on a beach in Galveston, Texas, some 1,300 miles from Charlottesville. He is the only person detained in connection with Graham's disappearance, charged with abduction with the intent to defile.

He has also been linked by forensic evidence to the case of Morgan Harrington, a 20-year-old Virginia Tech student who was last seen hitchhiking along U.S. 29 outside of Charlottesville in October 2009. She was found dead on a nearby farm the following January.

No arrests have been made in Harrington's case, and the cause of her death still is under investigation. Police, though, did recently seize a cab owned by Matthew that he was driving in Charlottesville in 2009, a source with knowledge of the investigation told CNN.

Matthew's next court appearance in relation to Graham's disappearance is scheduled for December 4.

Matthew's father, Jesse Matthew Sr., has said that his son would not have harmed Graham.

"For a big man, he's as gentle as they come," Jesse Matthew Sr. told CNN affiliate WTVR. "The only thing I could see, him, maybe trying to give the girl a ride or help her out. To kill or hurt somebody, that's not my son."

Matthew's Virginia-based lawyer, James Camblos, has declined to comment.