This repository contains data for a research project involving graph neural networks (GNNs) applied to mechanical metamaterials and their deformations. The mechanical metamaterials of interest consist of a flexible rubber-like material with a square grid of almost-circular holes in it, of various diameters. The holes are not quite circular, because they were made slightly elliptic to avoid the bifurcation point. This data was used to obtain the results in the paper 'Similarity Equivariant Graph Neural Networks for Homogenization of Metamaterials'. The data includes PyTorch Geometric Graph objects, raw data from MATLAB simulations, and files describing the finite element mesh. The Jupyter notebook 'data_create_graphs.ipynb' in the GitHub repository can be used to turn the raw data and mesh information into the graph objects. GitHub repository with the code: https://github.com/FHendriks11/SimEGNN Link to the corresponding paper Similarity Equivariant Graph Neural Networks for Homogenization of Metamaterials: https://www.sciencedirect.com/science/article/pii/S0045782525001392 (also on ArXiv: https://arxiv.org/abs/2404.17365) The .pkl files are pickle files and can be opened in Python using the standard pickle library. The mesh files, which have the extension .mat, are MatLab files and can be opened either in MatLab or in Python using scipy.io.loadmat from the scipy library.