Du Vrangr Gata (or The Wandering Path, in the Ancient Language), was the coalition of minor magicians who supported the Varden. Du Vrangr Gata was originally headed by the Twins, but following their apparent deaths after an Urgal ambush, Trianna took control. She was somewhat subdued, however, by Nasuada's firm administration and eventually the whole of the Du Vrangr Gata became answerable to Eragon.
After Galbatorix's defeat and Nasuada's elevation to the throne, the Du Vrangr Gata became the official spellcasters of the new kingdom and were charged with enforcing the rules on magic use throughout Alagaesia.
When Eragon tested the skills of the magicians of the Du Vrangr Gata, he discovered that most magicians were introduced to magic by a relative. Only a minority received an apprenticeship. The bulk of the group knew little of the ancient language, could not speak it fluently, as well as had their beliefs influenced by religious superstitions. He also found that slightly more than a third of the Du Vrangr Gata specialized as healers.
Du Vrangr Gata. Even their name betrays their ignorance. Correctly, in the Ancient Language, it is Du Gata Vrangr.— Eragon
Allegiance to the Varden
It's difficult to predict their actions even in the best of times. They might decide to oppose our authority for their own advantage.— Jörmundur
Although many of Du Vrangr Gata were loyal to the Varden, it was hinted that they were feared by the Varden because of the threat they posed.
When Nasuada requested Trianna to have Du Vrangr Gata manufacture lace to sell cheap within the Broddring Empire, she was trying to show Du Vrangr Gata that they were not an entity separate from the Varden. And though Trianna first disagreed with this proposal, Nasuada, exerting her authority over Trianna, convinced her that this would be an easy way for them to help pull the Varden out of their financial state. Nasuada then went on to request that Trianna select the brightest members of Du Vrangr Gata to be put to the task of inventing other magical techniques that would be beneficial to the Varden. In requesting this, as well as having Trianna repeatedly report back to her, Nasuada ensured that Du Vrangr Gata had remained under the influence and direction of the Varden.