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arXiv · 1804.06990

Weighted (Co)homology and Weighted Laplacian

Chengyuan Wu·Shiquan Ren·Jie Wu·Kelin Xia
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Abstract

In this paper, we generalize the combinatorial Laplace operator of Horak and Jost by introducing the $ϕ$-weighted coboundary operator induced by a weight function $ϕ$. Our weight function $ϕ$ is a generalization of Dawson's 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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Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia. 2023-05-21. Weighted (Co)homology and Weighted Laplacian. https://arxiv.org/abs/1804.06990

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