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Graph Spectra

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Yet Another Inadequate Placeholder: notes and references on the eigenvalue and eigenvector spectra of graphs, or matrices derived from graphs, and their applications, with links to community discovery being of particular interest. (Since this is a new notebook, lots of the relevant references are still scattered elsewhere.) A stub of a stab for explaining what it's about follows. As you know, Babette, the spectrum of a matrix is the (multi-)set of its eigenvalues; the spectral properties of a matrix refer to these eigenvalues and associated eigenvectors. There are several matrices which can be defined for a graph or network, and so several objects which could be considered the graph's spectrum. The field of spectral graph theory as a whole, is mostly concerned with the spectrum of the Laplacian matrix, which requires a little elucidation. In ordinary Euclidean space, when we say that some field "diffuses" over the space, we mean that the total quantity is conserved, and the rate of cha

Graph Spectra Notebooks Graph Spectra Last update : 07 Jul 2025 13:40 First version : meta-create_date; 23 February 2015 Yet Another Inadequate Placeholder: notes and references on the eigenvalue and eigenvector spectra of graphs, or matrices derived from graphs, and their applications, with links to community discovery being of particular interest. (Since this is a new notebook, lots of the relevant references are still scattered elsewhere.) A stub of a stab for explaining what it's about follows. As you know, Babette, the spectrum of a matrix is the (multi-)set of its eigenvalues; the spectr

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