tmQMg is a dataset of graph representation for neural networks – the natural quantum graph (NatQG), which are based on natural bond orbitals (NBOs) and their second-order perturbation analysis (SOPA). The combined use of NBOs and SOPA was used to build two different types of NatQG graphs: undirected (u-NatQG) and directed (d-NatQG) – both were informed with quantum electronic structure information included in node, edge, and whole-graph attribute vectors. Furthermore, we provide a baseline graph representation utilizing only periodic table properties.