cost vs involve

cost is a noun but involve is not a noun.

Word	Noun	Adjective	Verb	Adverb
cost	Yes	No	Yes	No
involve	No	No	Yes	No

As verbs, involve is a hypernym of cost; that is, involve is a word with a broader meaning than cost:

Other hypernyms of cost include ask, call for, demand, necessitate, need, postulate, require, take.

cost (noun)	involve (noun)
the property of having material worth (often indicated by the amount of money something would bring if sold)
value measured by what must be given or done or undergone to obtain something
the total spent for goods or services including money and time and labor

cost (verb)	involve (verb)
be priced at	make complex or intricate or complicated
require to lose, suffer, or sacrifice	occupy or engage the interest of
	have as a necessary feature
	connect closely and often incriminatingly
	contain as a part
	engage as a participant
	require as useful, just, or proper