2021/03/17 by Shiquan Ren, Chong Wang, Ren, Shiquan +1 · 1 citation
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2103.09552
openalex publication_date 2021/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2020, Alexander Grigor'yan, Yong Lin and Shing-Tung Yau [4] introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory. Based on the analytic torsion for digraphs introduced in [4], we consider the notion of weighted analytic torsion for vertex-weighted digraphs. For any non-vanishing real functions f and g on the vertex set, we consider the vertex-weighted digraphs with the weights (f,g). We calculate the (f,g)-weighted analytic torsion by examples and prove that the (f,g)-weighted analytic torsion only depend on the ratio f/g. In particular, if the weight is of the diagonal form (f,f), then the weighted analytic torsion equals to the usual (un-weighted) torsion.