Weighted (Co)homology and Weighted Laplacian
Chengyuan Wu, Shiquan Ren, Jie Wu, Kelin Xia · arXiv (Cornell University) · 2018
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.