Eigenvectors of Graph Laplacians: A Landscape
Eigenvectors of Graph Laplacians: A Landscape
We review the properties of eigenvectors for the graph Laplacian matrix,aiming at predicting a specific eigenvalue/vector from the geometryof the graph.We focus on eigenvectors that have zero components andextend the pioneering results of Merris (1998) on graph transformationsthat preserve a given eigenvalue $\lambda$ or shift it in a simple way.These …