2D materials, such as graphene monolayer or graphene nanoribbon, don’t really have a cross section. By definition, conductivity is $sigma = frac{J}{E}$, and $J$, the current density, is calculated per cross section: $J = frac{I}{A}$.
So how can conductivity (or resistivity, or current density) be reported for 2D materials if no actual cross section can be defined? To my understanding, only conductance (or resistance) can be assigned to 2D materials, as $G = frac{I}{V}$, which do not depend on cross section.