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To do so, we generalise charged signed graphs to $\\mathcal{L}$-graphs for appropriate finite sets $\\mathcal{L}$, and classify all $\\mathcal{L}$-graphs satisfying the same eigenvalue constraints. 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To do so, we generalise charged signed graphs to $\\mathcal{L}$-graphs for appropriate finite sets $\\mathcal{L}$, and classify all $\\mathcal{L}$-graphs satisfying the same eigenvalue constraints. 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