This image provided by the Galveston County Sheriff’s Office shows a booking photo of Jesse Leroy Matthew Jr. (AP)

The man accused of abducting University of Virginia student Hannah Graham has been linked to a 2005 sexual assault in Fairfax City via DNA evidence collected from one of the victim’s fingernails, according to court records.

The Virginia Department of Forensic Science’s comparison of DNA taken from Jesse L. Matthew Jr. and the sample taken from the woman at the time of the attack concluded that there is a “1 in greater than 7.2 billion” chance the DNA might belong to another person, according to the court records. Such a scientific finding, which eliminates almost the entire world population, probably will be central to the criminal case against Matthew.

The analysis was performed late last month after Matthew’s indictment on several charges related to the Sept. 24, 2005, attack on a 26-year-old woman in Fairfax City, court records show.

The woman was walking home from a supermarket about 10 p.m. when a man approached her from behind and grabbed her, authorities have said. The attacker carried the woman to a wooded area, where he sexually assaulted her. The man fled when a passerby startled him.

The sample collected from the victim jibes with a description of the attack that people with knowledge of the investigation gave The Washington Post. They said the woman vigorously fought her attacker and might have scratched his face; they described the suspect as possibly having scratches. Skin cells and blood from a scratch can provide enough evidence for a DNA match.

The victim in the Fairfax City case lives overseas, and attempts to reach her have been unsuccessful. The Post generally does not identify victims of sex crimes.

Matthew, 32, of Charlottesville has been charged with attempted capital murder, abduction with intent to defile and object sexual penetration in the case.

Matthew was arrested in Texas in September on charges related to the Graham case. Graham, 18, of Fairfax County, disappeared after she got lost during a night out in Charlottesville. Surveillance video showed Matthew following her and later with his arm around her.

Graham’s body was found on an abandoned property outside of Charlottesville last month. Matthew has been charged with abduction with intent to defile in her case. Frank Battle, an administrator with the office of the chief medical examiner, said Thursday that the investigation into the cause of death is ongoing.

James L. Camblos III, an attorney for Matthew, declined to comment on the DNA evidence because he had not seen the analysis. Dawn Butorac, the Fairfax County deputy public defender who also represents Matthew, and Commonwealth’s Attorney Ray Morrogh both declined to comment Thursday.

Authorities had said that forensic evidence also linked the Fairfax assault to the disappearance of Virginia Tech student Morgan Harrington. She vanished after leaving a Metallica concert on the U-Va. campus in 2009. Her body was discovered months later on a farm outside Charlottesville. People with knowledge of the investigation have told The Post that the cases were tied by DNA evidence.

Matthew is scheduled to appear in the Fairfax case Nov. 14.

Jennifer Jenkins contributed to this report.