Do i need to give back rent money if they leave early?

a renter of mine moved in , paid a month's rent and just moved out 7 days later. she had a rental agreement from me to sign for 4 days but never signed it, so no agreement. now the renter wants part of the money back. do i need to give any back ? i have not rented out to anyone else yet......very hard to do now. in the state of nevada. i feel the renter has forfeited the money for not giving a notice. it has been 8 days since