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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. 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