Number one fan (6)
But I've got no explanation for this one!
(Other definitions for egomaniac that I've seen before include "One who's self-obsessed" , "he thinks "it's all about ME"" , "Self-obsessed person" , "who's full of himself" , "number one fan" .)
(Other definitions for egoist that I've seen before include "Self-seeker" , "It goes with self-centred man" , "Selfish type" , "Man who thinks highly of himself" , "Conceited person with little regard for others" .)