Technique for notifying EIGRP neighbors when destroying adjacencies in a computer network

A technique efficiently notifies EIGRP neighbors when destroying adjacencies in a computer network. A goodbye notification packet is provided that enables an EIGRP router to inform one or more of its neighbors of its intention to destroy their existing adjacencies. The goodbye notification packet comprises an EIGRP packet header with variable-length fields embodied as an appended goodbye attribute. The appended goodbye attribute is illustratively tagged according to a TLV encoding format that defines a new type (T) field called "a goodbye" having a predetermined type that distinguishes it from a conventional EIGRP Hello packet. A value (V) field of information conveyed within the goodbye attribute contains a list of neighbor (peer) identifiers (IDs). The peer IDs on this list instruct those neighbor routers to "go away" so that their adjacencies can be destroyed.