Matrices in the Theory of Signed Simple Graphs

Abstract

I discuss the work of many authors on various matrices used to study signed graphs, concentrating on adjacency and incidence matrices and the closely related topics of Kirchhoff (`Laplacian') matrices, line graphs, and very strong regularity.

20 pp. Presented to the

Cited by in corpus (23)

• Spectral Properties of Complex Unit Gain Graphs
• An Oriented Hypergraphic Approach to Algebraic Graph Theory
• Applications of Structural Balance in Signed Social Networks
• Cheeger constants, structural balance, and spectral clustering analysis for signed graphs
• Constructing cospectral signed graphs
• Switching transformations for decentralized control of opinion patterns in signed networks: application to dynamic task allocation
• On cospectrality of gain graphs
• Gain-line graphs via $G$-phases and group representations
• Are Social Networks Really Balanced?
• Signatures, lifts, and eigenvalues of graphs
• Characterizations of line graphs in signed and gain graphs
• Open problems in the spectral theory of signed graphs
• Advances in Scaling Community Discovery Methods for Signed Graph Networks
• Spectral gaps, missing faces and minimal degrees
• The Hoffman program of graphs: old and new
• Some properties of Cayley signed graphs on finite abelian groups
• Unicyclic signed graphs with maximal energy
• On Adjacency Matrices and Descriptors of Signed Cycle Graphs
• On Products and Line Graphs of Signed Graphs, their Eigenvalues and Energy
• Resolution of Indecomposable Integral Flows on Signed Graphs
• On the Signed Complete Graphs with Maximum Index
• Energy of signed digraphs
• Induced subgraphs of product graphs and a generalization of Huang's theorem