Authors: Arsić, Branko
Cvetković, Dragoš
Simić, Slobodan 
Škarić, Milan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Graph spectral techniques in computer sciences
Journal: Applicable Analysis and Discrete Mathematics
Volume: 6
Issue: 1
First page: 1
Last page: 30
Issue Date: 1-Apr-2012
Rank: M21
ISSN: 1452-8630
DOI: 10.2298/AADM111223025A
We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indicate the fields in which it is used (e.g. in modelling and searching Internet, in computer vision, pattern recognition, data mining, multiprocessor systems, statistical databases, and in several other areas). We present some novel mathematical results (related to clustering and the Hoffman polynomial) as well.
Keywords: Complex networks | Computer science | Internet | Spectral clustering | Spectral graph theory
Publisher: School of Electrical Engineering, University of Belgrade
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Development of new information and communication technologies, based on advanced mathematical methods, with applications in medicine, telecommunications, power systems, protection of national heritage and education 

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