We propose an algorithm for determining the zeros of the electric conductivity in large molecular nanonstructures such as graphene sheets. To this end, we employ the inverse graph method, whereby non-zeros of the Green's functions are represented graphically by a segment connecting two atomic sites, to visually signal the existence of a conductance zero as a line that is missing. In rectangular graphene structures the topological properties of the inverse graph determine the existence of two types of Green's function zeros that correspond to absolute conductance cancellations with distinct behavior in the presence of external disorder. We discuss these findings and their potential applications in some particular cases.