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Jesse Leroy Matthew Jr, 32, has been charged with abduction with intent to defile Ms Graham, who has been missing since 13 September.
Thousands of volunteers had joined searches for the student, who was born in the UK but has lived in the US since she was five
Virginia State Police have said Matthew's arrest provided a "forensic link" to the 2009 unsolved murder of Morgan Harrington, a 20-year-old who also went missing from Charlottesville.
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'Nobody knows where my brother is' Watch
Nepal disaster toll rises to 39
Himalaya trekkers 'herded to deaths'
Relatives of Britons missing in Nepal after snowstorms hit have spoken of their relief that some have made contact to say they are safe.
Amanda Vardy said she had received the good news in an email from a tour company her brother, Nigel, was with.
Christopher Kneale, father of Clare Glazebrook, said he had also heard that his daughter's group was safe.
Others, who had been on trekking holidays, remain missing and a Facebook page has been set up to help find them.
At least 39 people have died in the storms and 150 have been injured, the Nepali authorities have said.
Ms Vardy had previously spoken of her concern for her brother who had been in "constant contact with the family" before communications suddenly stopped.
But she said she had now received an email which read: "All our team are fine and secure.
"They safely reached base camp. Don't worry, weather is getting better now."
Ms Vardy said: "The Britons that Nigel was with have all come back safe.
"We will get full confirmation when people have talked to him - so, good news.
"We just need now the 'Nigel is drinking whisky in a tent' and I'll be very happy."
Nigel Vardy's family had tried to persuade him to give up ice climbing, his sister said Ms Vardy said her family had tried to persuade her brother, who is from Belper in Derbyshire, to give up his ice climbing hobby.
On receiving an email that said his daughter Clare was safe, Mr Kneale said: "It is all we have got at the moment.
"We have to trust that.
"I don't know if they are continuing or coming home, that is up to them."
He said the wait for news had been "horrific".
The father of a Chesterfield woman in Nepal said he had received an email from a tour company saying she and her husband were safe at base camp.
He said he believed Mr Vardy was with them, although this has not been confirmed.
An unknown number of other Britons, many of them on trekking holidays, remain missing.
'Out of touch'
A BBC correspondent in Nepal said some people not heard from could be on other trekking routes where they were safe.
Many would be unable to contact their families even if they were not affected by the storms.
"Once they are on the mountains they are completely out of touch," BBC correspondent Andrew North said.
The Foreign Office said it had no information so far that any Britons were among the casualties.
It is advising those in the affected area to call their families and to check its online travel advice and social media for updates.
A spokesperson said: "We are in close contact with the local authorities, who are managing the rescue operation."
Mountaineer Alan Hinkes said many of those caught up in the storms would have been tourists.
"Normally the weather there is very pleasant. At the moment it must be horrendous. It seems they have been in white-out conditions," he said.
"If you get caught out in those conditions, which are almost Arctic, you've had it.
"There would have been trekkers not knowing what they were letting themselves in for."
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