  Commensurability oscillations in the magnetotransport of periodically
patterned systems, emerging from the interplay of cyclotron orbit and the
pattern periodicity, are a benchmark of mesoscopic physics in electron gas
systems. Exploiting similar effects in 2D materials would allow exceptional
control of electron behaviour, but is hindered by the requirement to maintain
ballistic transport over large length scales. Recent experiments have overcome
this obstacle and observed distinct magnetoresistance commensurability peaks
for perforated graphene sheets (antidot lattices). Interpreting the exact
mechanisms behind these peaks is of key importance, particularly in graphene
where a range of regimes are accessible by varying the electron density. In
this work a fully atomistic, device-based simulation of magnetoresistance
experiments allows us to analyse both the resistance peaks and the current flow
at commensurability conditions. Magnetoresistance spectra are found in
excellent agreement with experiment, but we show that a semi-classical
analysis, in terms of simple skipping or pinned orbits, is insufficient to
fully describe the corresponding electron trajectories. Instead, a generalised
mechanism in terms of states bound to individual antidots, or to groups of
antidots, is required. Commensurability features are shown to arise when
scattering between such states is enhanced. The emergence and suppression of
commensurability peaks is explored for different antidot sizes, magnetic field
strengths and electron densities. The insights gained from our study will guide
the design and optimization of future experiments with nanostructured graphene.

Mesoscale and Nanoscale Physics