  Graph states are the backbone of measurement-based continuous-variable
quantum computation. However, experimental realisations of these states induce
Gaussian measurement statistics for the field quadratures, which poses a
barrier to obtain a genuine quantum advantage. In this letter, we propose
mode-selective photon addition and subtraction as viable and experimentally
feasible pathways to introduce non-Gaussian features in such
continuous-variable graph states. In particular, we investigate how the
non-Gaussian properties spread among the vertices of the graph, which allows us
to show the degree of control that is achievable in this approach.
