Materials are physical networks where nodes and edges are spatially embedded physical objects that cannot overlap. Metamaterials are architected structures whose physical properties are determined primarily by geometry and connectivity rather than composition. They are typically built using structural elements with limited variability and predominantly local interactions, constraining their accessible property space. This raises a fundamental question: Can heterogeneous network designs enable mechanical properties beyond the reach of homogeneous systems? This work investigates this question through three studies: First, we introduce Scale-Rich (SR) metamaterials, generated through prescribed growth of variable thickness ligaments from random nucleation points, producing networks characterized by heterogeneous ligament lengths, thicknesses, and connectivity distributions. SR metamaterials exhibit tunable directional stiffness and wave velocities, delocalized nonlinear deformation, and enhanced energy absorption. Second, we develop a graph neural network-based framework that accelerates Force-Directed Layout (FDL) for embedding non-physical networks in physical space. This approach not only speeds up optimization but also discovers lower-energy configurations than traditional FDL. Beyond visualization, this method enables the physical embedding of arbitrary network connectivity, allowing for the generation of metamaterials. Finally, we propose to investigate the constraints determining which connectivity patterns can be physically realized as metamaterials. By identifying feasible adjacency matrices and embedding them via FDL, we systematically explore how topology and geometry jointly determine mechanical properties. This work aims to establish a framework for designing heterogeneous, network-based metamaterials and to understand how network architecture determines their properties.