Network Theory and the exploration of material space

The rapid growth in the quantity and quality of materials data enables machine learning to predict properties and guide the discovery of new materials, yet a comprehensive understanding of the materials space remains elusive. This presentation explores how network theory provides the tools to map that space and reveal its topology. Materials can be represented as nodes connected by chemical, structural, or functional similarity, forming networks that capture hidden correlations across materials databases. At the microscopic level, graph-based models encode atomic and molecular structures, while at higher scales, materials networks reveal similarity landscapes and synthesis pathways. We review recent results showing how topological descriptors uncover organization within complex datasets and discuss future perspectives where the integration of network science, machine learning, and automated laboratories forms a unified framework for exploring and expanding the materials universe.