Graph spectral techniques in computer sciences (Q2853261)

An extensive survey of graph spectral techniques used in computer sciences is presented. Some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and others), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs, etc., are described. For each of the described spectral technique it is indicated in which fields it is used (e.g., in modelling and searching the internet, in computer vision, pattern recognition, data mining, multiprocessor systems, statistical databases, and in several other areas). Moreover, some novel mathematical results (related to clustering and the Hoffman polynomial) are presented.