cock-a-hoop vs bragging

cock-a-hoop is not a noun while bragging is a noun.

Word	Noun	Adjective	Verb	Adverb
cock-a-hoop	No	Yes	No	No
bragging	Yes	Yes	No	No

As adjectives, cock-a-hoop and bragging are synonyms defined as:

Other synonyms of cock-a-hoop include big, boastful, braggart, braggy, crowing, self-aggrandising, self-aggrandizing.

cock-a-hoop (noun)	bragging (noun)
	an instance of boastful talk

cock-a-hoop (adjective)	bragging (adjective)
exhibiting self-importance	exhibiting self-importance