Graph representation of multi-dimensional materials

Abstract The integration of graph-based representations with machine learning methodologies is transforming the landscape of material discovery, offering a flexible approach for modelling a variety of materials, from molecules and nanomaterials to expansive three-dimensional bulk materials. Nonetheless, the literature often lacks a systematic exploration from the perspective of material dimensionality. While it is important to design representations and algorithms that are universally applicable across species, it is intuitive for material scientists to align the underlying patterns between dimensionality and the characteristics of the employed graph descriptors. In this review, we provide an overview of the graph representations as inputs to machine learning models and navigate the recent applications, spanning the diverse range of material dimensions. This review highlights both persistent gaps and innovative solutions to these challenges, emphasising the pressing need for larger benchmark datasets and leveraging graphical patterns. As graph-based machine learning techniques evolve, they present a promising frontier for accurate, scalable, and interpretable material applications.