This dataset supports the paper: "Exploring the configurational space of amorphous graphene with machine-learned atomic energies" (https://doi.org/10.1039/D2SC04326B). Trajectory data for the 200-atom structures (Fig. 3) and the final configurations for the 612-atom structures as well as the GAP-17-optimised 610-atom structure from Toh et al are provided (Fig. 4). Additionally, the structures used for data analysis in Fig. 5 are given. The files are in extended xyz (.xyz) format and contain the raw data for coordinates, forces, and atomic energies (labelled 'c_1'). The files also contain the atomic energies relative to pristine graphene, labelled "Energy_per_atom", and the locally averaged energy relative to pristine graphene, labelled "NN_Energy_per_atom". Topological information is included at the end of the .xyz file for the 612-atom structures ('fig_4'/) and for the structures in 'fig_5/'. All raw atomic energies were computed using LAMMPS default settings and were output with six significant figures, with the exception of the Toh et al. structure (for which ASE was used, outputting a higher number of significant figures). The data can be read using, for example, the Atomic Simulation Environment (ASE), or visualised using Ovito.