letter of the alphabet vs graph

letter of the alphabet and graph both are nouns.

Word	Noun	Adjective	Verb	Adverb
letter of the alphabet	Yes	No	No	No
graph	Yes	No	Yes	No

As nouns, graph is a hypernym of letter of the alphabet; that is, graph is a word with a broader meaning than letter of the alphabet:

letter of the alphabet: the conventional characters of the alphabet used to represent speech
graph: a written symbol that is used to represent speech

Other hypernyms of letter of the alphabet include character, grapheme, graphic symbol.

letter of the alphabet (noun)	graph (noun)
the conventional characters of the alphabet used to represent speech	a visual representation of the relations between certain quantities, represented as points, plotted with reference to a set of axes
	a visual display of information
	a written symbol that is used to represent speech

letter of the alphabet (verb)	graph (verb)
	represent by means of a graph
	plot upon a graph