BaryGraph introduces a fundamental shift in knowledge graph design: every relationship exists as its own embedded document, called a BaryEdge, rather than as metadata on an edge between nodes. Each BaryEdge carries a vector derived from the connected concepts, their connection quality, and a contextual embedding of the relationship type. This structure enables recursive pairing — two BaryEdges at the same level are bridged by a third one level below, forming "MetaBary" triads that surface structural bridges between concepts distant in embedding space.
The system runs locally on MongoDB Community with mongot and nomic-embed-text, ingesting the full English Wiktionary's 6.6 million documents. An MCP server is live for experimentation, and preprints with benchmark CSVs are available on Zenodo.
Standard vector search treats relationships as byproducts of proximity, discarding relational information. BaryGraph's approach preserves it. In tests on SimLex-999 and WordSim-353, raw cosine similarity showed near-zero correlation with human judgments (ρ ≈ −0.04), while structural metrics — shared BaryEdges and relational neighborhood overlap — correlated meaningfully. The forest topology (each node has at most one parent) allows root traversal via a single $graphLookup without cycle handling.
For developers building RAG systems, knowledge graphs, or semantic search, this suggests relational structure may carry more signal than embedding proximity alone.
