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Example

Graph <N_5, E> where E = {<0, 1>, <1, 2>, <1, 3>, <2, 3>, <3, 4>}

reflexiveN5(E) = E union {<0, 0>, <1, 1>, <2, 2>, <3, 3>, <4, 4>}

transitiveN5(E) =

{<0, 1>, <0, 2>, <0, 3>, <0, 4>, <1, 2>, <1, 3>, <1, 4>, <2, 3>, <2, 4>}