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Given a graph $G$ on $n$ vertices, one may associate to it the element \\[ X_G=\\sum_{ij\\in E(G)} (ij)\\in \\C[S_n]. \\] The action of $X_G$ in irreducible representations of $S_n$ produces spectral invariants of graphs. The standard representation $(n-1,1)$ recovers the ordinary graph Laplacian spectrum, up to the elementary affine change $X_G=mI-L_G$, where $m=|E(G)|$. The next component, $(n-2,2)$, gives the first representation-theoretic correction. 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