Oriented hypergraphs: introduction and balance

zbMath1295.05169arXiv1210.0943MaRDI QIDQ396889

Lucas J. Rusnak

Publication date: 14 August 2014

Published in: The Electronic Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.0943

zbMATH Keywords

balanced matrixbalanced hypergraphoriented hypergraphsigned hypergraph

Mathematics Subject Classification ID

Hypergraphs (05C65) Structural characterization of families of graphs (05C75) Signed and weighted graphs (05C22)

Related Items (22)

A connection between Hadamard matrices, oriented hypergraphs and signed graphs ⋮ Oriented hypergraphs: balanceability ⋮ A spectral method to incidence balance of oriented hypergraphs and induced signed hypergraphs ⋮ Unnamed Item ⋮ Graphs, Simplicial Complexes and Hypergraphs: Spectral Theory and Topology ⋮ A characterization of oriented hypergraphic Laplacian and adjacency matrix coefficients ⋮ Computational graph completion ⋮ Unnamed Item ⋮ Oriented hypergraphs: introduction and balance ⋮ Incidence hypergraphs: the categorical inconsistency of set-systems and a characterization of quiver exponentials ⋮ An oriented hypergraphic approach to algebraic graph theory ⋮ Coloring the normalized Laplacian for oriented hypergraphs ⋮ Unnamed Item ⋮ Signed \(k\)-uniform hypergraphs and tensors ⋮ Spectral theory of Laplace operators on oriented hypergraphs ⋮ Sharp bounds for the largest eigenvalue ⋮ A characterization of oriented hypergraphic balance via signed weak walks ⋮ Incidence hypergraphs: injectivity, uniformity, and matrix-tree theorems ⋮ Oriented hypergraphic matrix-tree type theorems and bidirected minors via Boolean order ideals ⋮ Characterizing attitudinal network graphs through frustration cloud ⋮ Spectra of cycle and path families of oriented hypergraphs ⋮ Pruned inside-out polytopes, combinatorial reciprocity theorems and generalized permutahedra

Uses Software

• Leibniz

Cites Work

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• Oriented hypergraphs: introduction and balance
• An oriented hypergraphic approach to algebraic graph theory
• Biased graphs. I: Bias, balance, and gains
• Signed graphs
• Alpha-balanced graphs and matrices and GF(3)-representability of matroids
• Orientation of signed graphs
• A characterization of signed hypergraphs and its applications to VLSI via minimization and logic synthesis
• Decomposition of balanced matrices
• Combinatorial optimization. Polyhedra and efficiency (3 volumes)
• Balanced matrices
• On the notion of balance of a signed graph

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