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A Brief Introduction to Spectral Graph Theory

2018 Eigenvalues
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Release : 2018
Genre : Eigenvalues
Kind : eBook
Book Rating : 880/5 ( reviews)

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Book Synopsis A Brief Introduction to Spectral Graph Theory by : Bogdan Nica

Download or read book A Brief Introduction to Spectral Graph Theory written by Bogdan Nica. This book was released on 2018. Available in PDF, EPUB and Kindle. Book excerpt: "Spectral graph theory starts by associating matrices to graphs - notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained"--Back cover.

A Brief Introduction to Spectral Graph Theory

MATHEMATICS
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Release :
Genre : MATHEMATICS
Kind : eBook
Book Rating : 885/5 ( reviews)

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Book Synopsis A Brief Introduction to Spectral Graph Theory by : Bogdan Nica

Download or read book A Brief Introduction to Spectral Graph Theory written by Bogdan Nica. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt: Spectral graph theory starts by associating matrices to graphs – notably, the adjacency matrix and the Laplacian matrix. The general theme is then, firstly, to compute or estimate the eigenvalues of such matrices, and secondly, to relate the eigenvalues to structural properties of graphs. As it turns out, the spectral perspective is a powerful tool. Some of its loveliest applications concern facts that are, in principle, purely graph theoretic or combinatorial. This text is an introduction to spectral graph theory, but it could also be seen as an invitation to algebraic graph theory. The first half is devoted to graphs, finite fields, and how they come together. This part provides an appealing motivation and context of the second, spectral, half. The text is enriched by many exercises and their solutions. The target audience are students from the upper undergraduate level onwards. We assume only a familiarity with linear algebra and basic group theory. Graph theory, finite fields, and character theory for abelian groups receive a concise overview and render the text essentially self-contained.

An Introduction to the Theory of Graph Spectra

2009-10-15 Mathematics
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Release : 2009-10-15
Genre : Mathematics
Kind : eBook
Book Rating : 088/5 ( reviews)

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Book Synopsis An Introduction to the Theory of Graph Spectra by : Dragoš Cvetković

Download or read book An Introduction to the Theory of Graph Spectra written by Dragoš Cvetković. This book was released on 2009-10-15. Available in PDF, EPUB and Kindle. Book excerpt: This introductory text explores the theory of graph spectra: a topic with applications across a wide range of subjects, including computer science, quantum chemistry and electrical engineering. The spectra examined here are those of the adjacency matrix, the Seidel matrix, the Laplacian, the normalized Laplacian and the signless Laplacian of a finite simple graph. The underlying theme of the book is the relation between the eigenvalues and structure of a graph. Designed as an introductory text for graduate students, or anyone using the theory of graph spectra, this self-contained treatment assumes only a little knowledge of graph theory and linear algebra. The authors include many new developments in the field which arise as a result of rapidly expanding interest in the area. Exercises, spectral data and proofs of required results are also provided. The end-of-chapter notes serve as a practical guide to the extensive bibliography of over 500 items.

Spectral Graph Theory

1997 Mathematics
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Release : 1997
Genre : Mathematics
Kind : eBook
Book Rating : 158/5 ( reviews)

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Book Synopsis Spectral Graph Theory by : Fan R. K. Chung

Download or read book Spectral Graph Theory written by Fan R. K. Chung. This book was released on 1997. Available in PDF, EPUB and Kindle. Book excerpt: This text discusses spectral graph theory.

Graph Spectra for Complex Networks

2010-12-02 Technology & Engineering
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Release : 2010-12-02
Genre : Technology & Engineering
Kind : eBook
Book Rating : 276/5 ( reviews)

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Book Synopsis Graph Spectra for Complex Networks by : Piet van Mieghem

Download or read book Graph Spectra for Complex Networks written by Piet van Mieghem. This book was released on 2010-12-02. Available in PDF, EPUB and Kindle. Book excerpt: Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.

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