Spectral Graph Theory
Eigenvalues of adjacency and Laplacian matrices, Cheeger inequalities.
Spectral Graph Theory. Eigenvalues of adjacency and Laplacian matrices, Cheeger inequalities.
Foundations and canonical references
The standard treatments of spectral graph theory approach the subject from complementary angles. Chung, Spectral Graph Theory (1997) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Brouwer, Spectra of Graphs (2012) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for spectral graph theory include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 1997Spectral Graph Theorychung-1997
- textbook · primary · 2012Spectra of Graphsbrouwer-2012, haemers-2012
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