The vagus nerve is part of the group of cranial nerves responsible for innervation of structures derived from the branchial arches. It is also part of a group together with the glossopharyngeal and accessory nerves that passes through the jugular foramen which is termed the vagus group.he accessory nerve is part of the group of cranial nerves responsible for innervation of structures derived from the branchial arches. It is also part of a group together with the glossopharyngeal and vagus nerves that passes through the jugular foramen which is termed the vagus group.