2018/04/19 by Wu, Chengyuan, Ren, Shiquan, Wu, Jie +1
#Algebraic Topology (math.AT) #FOS: Mathematics
paper · doi:10.48550/arxiv.1804.06990
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.