Simplicial networks and effective resistance

DOI10.1016/j.aam.2018.05.004zbMath1393.05316OpenAlexW2805036820MaRDI QIDQ1661482

Kang-Ju Lee, Woong Kook

Publication date: 16 August 2018

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2018.05.004

zbMATH Keywords

effective resistancecombinatorial Hodge theorycombinatorial Laplacianshigh-dimensional tree-numberssimplicial network

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Applications of graph theory to circuits and networks (94C15) Combinatorial aspects of simplicial complexes (05E45)

Related Items (6)

Persistent Laplacians: Properties, Algorithms and Implications ⋮ Sombor index and degree-related properties of simplicial networks ⋮ Hodge Laplacians on Graphs ⋮ Kirchhoff index of simplicial networks ⋮ High-dimensional networks and spanning forests ⋮ Biomolecular topology: modelling and analysis

Cites Work

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• Enumeration of \({\mathbb{Q}}\)-acyclic simplicial complexes
• Resistances and currents in infinite electrical networks
• Counting colorful multi-dimensional trees
• Computing Betti numbers via combinatorial Laplacians
• Kirchhoff's theorems in higher dimensions and Reidemeister torsion
• Harmonic functions and boundary value problems on a chain complex
• Simplicial matrix-tree theorems
• Algebraic Potential Theory on Graphs

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