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big head

1. Informal Conceit; egotism.
2. also big·head (bĭg′hĕd′) Any of various diseases of animals, especially rams, characterized by swelling of the head, face, or neck.

big′head′ed adj.
big′head′ed·ness n.
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Informal. An exaggerated belief in one's own importance:
Informal: bighead, swelled head.
References in periodicals archive ?
Two of the portraits at the Pompidou, those of Pierre Matisse (Dubuffet's New York dealer) and Michel Tapie (the art critic), render the model's head as a giant pancake, though that is no indication of either man's bigheadedness. Dubuffet liked, as he put it, to "inscribe faces which are in reality gaunt and angular inside a roughly circular shape, the form of a gourd or a tart." This pancaking of the model's head could be comical or mystifying, and in the case of Michel Tapie soleil it is decidedly the latter.
Broadcaster Sandi Toksvig "It is this sort of bigheadedness and contempt for public money that gets MPs a bad name."
A s to that, Houllier's most caustic remark concerned the player's perceived bigheadedness.