Apart from assessing individual asset performance, investors in financial markets also need to consider how a set of firms performs collectively as a portfolio. Whereas traditional Markowitz-based mean-variance portfolios are widespread, network-based optimisation techniques offer a more flexible tool to capture complex interdependencies between asset values. However, most of the existing studies do not contain firms at risk of default and remove any firms that drop off indices over a certain time. This is the first study to also incorporate such firms in portfolio optimisation on a large scale. We propose and empirically test a novel method that leverages Graph Attention networks (GATs), a subclass of Graph Neural Networks (GNNs). GNNs, as deep learning-based models, can exploit network data to uncover nonlinear relationships. Their ability to handle high-dimensional data and accommodate customised layers for specific purposes makes them appealing for large-scale problems such as mid- and small-cap portfolio optimisation. This study utilises 30 years of data on mid-cap firms, creating graphs of firms using distance correlation and the Triangulated Maximally Filtered Graph approach. These graphs are the inputs to a GAT model incorporating weight and allocation constraints and a loss function derived from the Sharpe ratio, thus focusing on maximising portfolio risk-adjusted returns. This new model is benchmarked against a network characteristic-based portfolio, a mean variance-based portfolio, and an equal-weighted portfolio. The results show that the portfolio produced by the GAT-based model outperforms all benchmarks and is consistently superior to other strategies over a long period, while also being informative of market dynamics.