In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the $phi$-weighted coboundary operator induced by a weight function $phi$. Our weight function $phi$ is a generalization of Dawsons weighted boundary map. We show that our above-mentioned generalizations include new cases that are not covered by previous literature. Our definition of weighted Laplacian for weighted simplicial complexes is also applicable to weighted/unweighted graphs and digraphs.
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