commune vs intercommunicate

commune is a noun but intercommunicate is not a noun.

Word	Noun	Adjective	Verb	Adverb
commune	Yes	No	Yes	No
intercommunicate	No	No	Yes	No

As verbs, intercommunicate is a hypernym of commune; that is, intercommunicate is a word with a broader meaning than commune:

commune: communicate intimately with; be in a state of heightened, intimate receptivity
intercommunicate: transmit thoughts or feelings

Other hypernyms of commune include communicate.

commune (noun)	intercommunicate (noun)
a body of people or families living together and sharing everything
the smallest administrative district of several European countries

commune (verb)	intercommunicate (verb)
receive Communion, in the Catholic church	transmit thoughts or feelings
communicate intimately with; be in a state of heightened, intimate receptivity	be interconnected, afford passage