randomness vs unregularity

randomness and unregularity both are nouns.

Word	Noun	Adjective	Verb	Adverb
randomness	Yes	No	No	No
unregularity	Yes	No	No	No

As nouns, unregularity is a hypernym of randomness; that is, unregularity is a word with a broader meaning than randomness:

randomness: the quality of lacking any predictable order or plan
unregularity: not characterized by a fixed principle or rate; at irregular intervals

Other hypernyms of randomness include irregularity.

randomness (noun)	unregularity (noun)
the quality of lacking any predictable order or plan	not characterized by a fixed principle or rate; at irregular intervals
(thermodynamics) a thermodynamic quantity representing the amount of energy in a system that is no longer available for doing mechanical work