We challenge black-box purely deep neural approaches for molecules and graph generation, which are limited in controllability and lack formal guarantees. We introduce Neuro-Symbolic Graph Generative Modeling (NSGGM), a neurosymbolic framework that reapproaches molecule generation as a scaffold and interaction learning task with symbolic assembly. An autoregressive neural model proposes scaffolds and refines interaction signals, and a CPU-efficient SMT solver constructs full graphs while enforcing chemical validity, structural rules, and user-specific constraints, yielding molecules that are correct by construction and interpretable control that pure neural methods cannot provide. NSGGM delivers strong performance on both unconstrained generation and constrained generation tasks, demonstrating that neuro-symbolic modeling can match state-of-the-art generative performance while offering explicit controllability and guarantees. To evaluate more nuanced controllability, we also introduce a Logical-Constraint Molecular Benchmark, designed to test strict hard-rule satisfaction in workflows that require explicit, interpretable specifications together with verifiable compliance.

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