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  3. Graph Spectra for Complex Networks
Publisher:
Cambridge University Press
Online publication date:
September 2023
Print publication year:
2023
Online ISBN:
9781009366793
DOI:
https://doi.org/10.1017/9781009366793
Subjects:
Algorithmics, Complexity, Computer Algebra, Computational Geometry, Communications and Signal Processing, Engineering, Computer Science
Information

Book 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.

Reviews

‘This book provides a comprehensive background in the area, especially for researchers and graduate students … Highly recommended.’

J. T. Saccoman Source: CHOICE

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