We propose a multilayered symbolic framework for general graph classification that leverages sparse binary hypervectors and Tsetlin Machines. Each graph is encoded through structured message passing, where node, edge, and attribute information are bound and bundled into a symbolic hypervector. This process preserves the hierarchical semantics of the graph through layered binding from node attributes to edge relations to structural roles resulting in a compact, discrete representation. We also formulate a local interpretability framework which lends itself to a key advantage of our approach being locally interpretable. We validate our method on TUDataset benchmarks, demonstrating competitive accuracy with strong symbolic transparency compared to neural graph models.