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• W2897734398 abstract "Weighted hypergraphs are generalizations of weighted simplicial complexes. In recent years, weighted Laplacians of weighted simplicial complexes have been studied. In 2016, as a generalization of the homology of simplicial complexes, the embedded homology of hypergraphs was constructed. In this paper, we generalize the weighted Laplacians of weighted simplicial complexes to weighted hypergraphs. We study the relations between the weighted Laplacians and the weighted embedded homology of weighted hypergraphs. We generalize the Hodge decompositions of weighted simplicial complexes to weighted hypergraphs. Moreover, as a complement for the Hodge decompositions, we give some results for the nonzero eigenvalues of the weighted Laplacians of weighted hypergraphs." @default.
• W2897734398 created "2018-10-26" @default.
• W2897734398 creator A5018703109 @default.
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• W2897734398 date "2018-05-29" @default.
• W2897734398 modified "2023-09-25" @default.
• W2897734398 title "Hodge Decompositions for Weighted Hypergraphs" @default.
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• W2897734398 doi "https://doi.org/10.48550/arxiv.1805.11331" @default.
• W2897734398 hasPublicationYear "2018" @default.
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