The victims were mainly students and police in Leeds are investigating seven incidents, most of which took place between 8pm and 8.30pm.
Police say a gang that was 10 to 15 strong, the members of which had their faces covered, were behind the incidents on Wednesday night in the Woodhouse area of the city.
In some cases the victims were threatened into handing over their valuables and some were assaulted resulting in injuries. Two of the victims required hospital treatment.
Detectives are also investigating whether the muggings are linked to robberies in Woodhouse over the Bonfire Night weekend.
Parents are becoming increasingly concerned about the attacks and yesterday a meeting was held in Headingley at which police said six men had been arrested.
Police have said there is nothing to suggest the victims were specifically targeted for being students.
A West Yorkshire Police spokesman said those arrested were aged 14 to 19, and they were in custody. Inquiries to trace other suspects are continuing.
He said: “Extra officers from across North West Leeds Division were drafted into the area last night to carry out high-visibility patrols to reassure people in the community and to deter any further offences.
“This activity will be continuing over the coming nights.”
One parent, John McNamara, whose son Danny, a student, was attacked near a hall of residence said: “He was smashed on his head from behind, knocked to the floor and stamped and kicked all over his body and head.”
Police have told him he is lucky no weapons were used in the assault.
Wednesday night’s incidents occurred in Leicester Place, Clarkson View, Hartley Crescent, St Mark’s Road, St Mark’s Street, Hartley Avenue, and Burchett Place.