Graph spectra in Computer Science

In this paper, we shall give a survey of applications of the theory of graph spectra to Computer Science. Eigenvalues and eigenvectors of several graph matrices appear in numerous papers on various subjects relevant to information and communication technologies. In particular, we survey applications...

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Bibliographic Details
Published in:Linear algebra and its applications Vol. 434; no. 6; pp. 1545 - 1562
Main Authors: CVETKOVIC, Dragoš, SIMIC, Slobodan
Format: Journal Article
Language:English
Published: Amsterdam Elsevier Inc 15.03.2011
Elsevier
Subjects:
Algebra
Applications
Applied sciences
Combinatorics
Combinatorics. Ordered structures
Communication technology
Complex networks
Computer Science
Computer science; control theory; systems
Exact sciences and technology
Graph spectra
Graph theory
Information retrieval. Graph
Information technology
Internet
Linear and multilinear algebra, matrix theory
Mathematics
Sciences and techniques of general use
Theoretical computing
68M07
68U10
Graph spectra
05C50
Applications
Graph theory
Communication technology
Information technology
15A18
15A51
81P68
Computer Science
Complex networks
65F15
Internet
68R10
68P20
Modeling
Spectrum
Multiprocessor
Database
Eigenvalue problem
Computer vision
Statistical analysis
Probabilistic approach
Stochastic matrix
Eigenvector
Cubic graph
Data processing
ISSN:0024-3795
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Summary:In this paper, we shall give a survey of applications of the theory of graph spectra to Computer Science. Eigenvalues and eigenvectors of several graph matrices appear in numerous papers on various subjects relevant to information and communication technologies. In particular, we survey applications in modeling and searching Internet, in computer vision, data mining, multiprocessor systems, statistical databases, and in several other areas. Some related new mathematical results are included together with several comments on perspectives for future research. In particular, we claim that balanced subdivisions of cubic graphs are good models for virus resistent computer networks and point out some advantages in using integral graphs as multiprocessor interconnection networks.
ISSN:0024-3795
DOI:10.1016/j.laa.2010.11.035