Hybrid organic-inorganic glasses exhibit unique electro-optical properties along with excellent thermal stability. Their inherently mechanically fragile nature, however, which derives from the oxide component of the hybrid glass network together with the presence of terminal groups that reduce network connectivity, remains a fundamental challenge for their integration in nanoscience and energy technologies. We report on a combined synthesis and computational strategy to elucidate the effect of molecular structure on mechanical properties of hybrid glass films. We first demonstrate the importance of rigidity percolation to elastic behavior. Secondly, using a novel application of graph theory, we reveal the complex 3-D fracture path at the molecular scale and show that fracture energy in brittle hybrid glasses is fundamentally governed by the bond percolation properties of the network. The computational tools and scaling laws presented provide a robust predictive capability for guiding precursor selection and molecular network design of advanced hybrid organic-inorganic materials.