  Nearly complete intersection ideals were introduced by A. Boocher and J.
Seiner (2018) and defines a special class of monomial ideals in a polynomial
ring. These ideals were used to give a lower bound of the total sum of betti
numbers that appear a minimal free resolution of a monomial ideal. In this note
we give a graph theoretic classification of nearly complete intersection ideals
generated in degree two. In doing so, we define a novel graph operation (the
inversion) that is motivated by the definition of this new class of ideals.
