administration vs incumbency

administration and incumbency both are nouns.

Word	Noun	Adjective	Verb	Adverb
administration	Yes	No	No	No
incumbency	Yes	No	No	No

As nouns, incumbency is a hypernym of administration; that is, incumbency is a word with a broader meaning than administration:

Other hypernyms of administration include tenure, term of office.

administration (noun)	incumbency (noun)
a method of tending to or managing the affairs of some group of people (especially the group's business affairs)	the office of an incumbent
the act of administering medication	a duty that is incumbent upon you
the act of meting out justice according to the law	the term during which some position is held
the act of governing; exercising authority
the persons (or committees or departments etc.) who make up a body for the purpose of administering something
the tenure of a president