Recent advances in computational chemistry, machine learning, and large-scale virtual screening have rapidly expanded the accessible chemical space, increasing the need for interpretable molecular representations that capture the hierarchical topological structure of molecules. Existing formats, such as Simplified Molecular Input Line Entry System (SMILES) strings and MOL files, effectively encode molecular graphs but provide limited support for representing the multi-level structural information needed for complex downstream tasks. To address these challenges, we introduce HiFrAMes, a novel graph–theoretic hierarchical molecular fragmentation framework that decomposes molecular graphs into chemically meaningful substructures and organizes them into hierarchical scaffold representations. HiFrAMes is implemented as a four-stage pipeline consisting of leaf and ring chain extraction, ring mesh reduction, ring enumeration, and linker detection, which iteratively transforms raw molecular graphs into interpretable abstract objects. The framework decomposes molecules into chains, rings, linkers, and scaffolds while retaining global topological relationships. We apply HiFrAMes to both complex and drug-like molecules to generate molecular fragments and scaffold representations that capture structural motifs at multiple levels of abstraction. The resulting fragments are evaluated using selection criteria established in the fragment-based drug discovery literature and qualitative case studies to demonstrate their suitability for downstream computational tasks.