Eigenvectors of graph Laplacians: a landscape
Salón 203 del Edificio Anexo del IIMAS Circuito Escolar S/N, Ciudad Universitaria,, Ciudad de México, Coyoacán, MexicoColoquio de Matemáticas Aplicadas We review the properties of eigenvectors for the graph Laplacian matrix, aiming at predicting a specific eigenvalue/vector from the geometry of the graph. We focus on eigenvectors that have zero components and extend the pioneering results of Merris (1998) on graph transformations that preserve a given eigenvalue $\lambda$ or shift it […]