Big head and Self-importance

Self-importance and big head are semantically related. In some cases you can use "Self-importance" instead a noun phrase "Big head".

Self-importance noun - An exaggerated sense of one's importance that shows itself in the making of excessive or unjustified claims.

Big head and self-importance are semantically related. Sometimes you can replace phrase "Big head" with "Self-importance", this phrases are similar.