  We present a systematic classification of the elementary excitations of
Bose-Einstein condensates in cylindrical traps in terms of their shapes. The
classification generalizes the concept of families of excitations first
identified by Hutchinson and Zaremba (1998) Phys. Rev. A 57 1280 by introducing
a second classification number that allows all possible modes to be assigned to
a family. We relate the energy ordering of the modes to their family
classification, and provide a simple model which explains the relationship.
