We present an interpretable network-based framework for representing idiomatic and figurative meaning across eight typologically diverse languages, totaling 160 conventional expressions, the large majority of which are idiomatic. Each expression is annotated with binary conceptual features (containment, concealment, emotional, social, etc.) derived from cognitive-linguistic theory, and pairwise Jaccard similarities define a weighted graph. Community detection reveals that idioms cluster by conceptual schema rather than by language, producing a structure consistent with cognitive-linguistic predictions. The conceptual network captures unique semantic information not present in distributional embeddings, can be scaled via automatic annotation with LLMs, improves downstream idiom detection, and remains robust when enriched with corpus frequencies. Cross-lingual transfer experiments show that conceptual proximity alone can identify acceptable translation equivalents across five language families, with substantial gains over embedding-based baselines. Ablation studies demonstrate that all three feature dimensions -- schemas, roles, and valence -- contribute non-redundantly to both the network's organizational properties and its performance on idiom detection, and that specific graph-derived signals (community membership, neighbor similarity) are particularly informative. The framework offers an interpretable, cross-linguistically stable representation of idiomatic meaning, combining theoretical grounding with practical utility.

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