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Every pair of $s$-sets $I$ and $J$ is associated with a weight $w(I,J)$, which is the number of edges in $H$ passing through $I$ and $J$ if $I\\cap J=\\emptyset$, and 0 if $I\\cap J\\not=\\emptyset$. The $s$-th Laplacian $\\L^{(s)}$ of $H$ is defined to be the normalized Laplacian of $G^{(s)}$. 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