Spectral Graph Drawing: a Survey

Graph Drawing is the science of finding an intuitive visualization of a network (or in mathematical terms of a graph). One approach is to define energy functions that represent design criteria for graph layouts. It happens to be that the eigenvalues of graph related matrices are locally optimal solutions for some of the energy functions. Using the eigenvalues for a graph layout is called Spectral Graph Drawing. This book is a survey of Spectral Graph Drawing methods. Graph layouts of several graph-related matrices, such as the adjacency or the Laplace matrix, are studied. There is a special section on the implementation of the graph layouts using the power iteration. At the end the focus is extended to the special requirements for Dynamic Spectral Graph Drawing, i. e. time-variant graphs are drawn with spectral methods.