Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge Decompositions for Weighted Hypergraphs   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.

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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph