ENGLISH

Graph Spectra for Complex Networks

By Piet Van Mieghem

Book information

Publisher
Cambridge University Press
Year
2023
ISBN
1009366807, 9781009366809, 9781009366793
DOI
10.1017/9781009366793
ASIN
B0CG2CVG7F
UDC
519.1
LBC
22.176
LCC
QA166 .V365 2023
Language
english
Format
PDF
Filesize
7 MB (7017991 bytes)
Edition
2
Pages
535\536
Orientation
portrait
Paginated
no
Scanned
no
Time added
2023-11-17 17:07:26
Graph Theory; System Analysis; Algorithmics; Compl

Description

This concise and self-contained introduction builds up the spectral theory of graphs from scratch, with linear algebra and the theory of polynomials developed in the later parts. The book focuses on properties and bounds for the eigenvalues of the adjacency, Laplacian and effective resistance matrices of a graph. The goal of the book is to collect spectral properties that may help to understand the behavior or main characteristics of real-world networks. The chapter on spectra of complex networks illustrates how the theory may be applied to deduce insights into real-world networks. The second edition contains new chapters on topics in linear algebra and on the effective resistance matrix, and treats the pseudoinverse of the Laplacian. The latter two matrices and the Laplacian describe linear processes, such as the flow of current, on a graph. The concepts of spectral sparsification and graph neural networks are included.

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