The Mathematics of Finite Networks: An Introduction to Operator Graph Theory

Michael Rudolph

doi:10.1017/9781316466919

The Mathematics of Finite Networks

An Introduction to Operator Graph Theory

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Carmona, Ángeles and Encinas, Andrés M. 2025. Inverse Problems, Regularization Methods and Related Topics. p. 213.

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Michael Rudolph, Centre National de la Recherche Scientifique (CNRS), Tours

Publisher:: Cambridge University Press
Online publication date:: April 2022
Print publication year:: 2022
Online ISBN:: 9781316466919
DOI:: https://doi.org/10.1017/9781316466919

Subjects:: Algorithmics, Complexity, Computer Algebra, Computational Geometry, Physics and Astronomy, Computer Science, Statistical Physics

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Since the early eighteenth century, the theory of networks and graphs has matured into an indispensable tool for describing countless real-world phenomena. However, the study of large-scale features of a network often requires unrealistic limits, such as taking the network size to infinity or assuming a continuum. These asymptotic and analytic approaches can significantly diverge from real or simulated networks when applied at the finite scales of real-world applications. This book offers an approach to overcoming these limitations by introducing operator graph theory, an exact, non-asymptotic set of tools combining graph theory with operator calculus. The book is intended for mathematicians, physicists, and other scientists interested in discrete finite systems and their graph-theoretical description, and in delineating the abstract algebraic structures that characterise such systems. All the necessary background on graph theory and operator calculus is included for readers to understand the potential applications of operator graph theory.

‘The tool provided in this book is potentially valuable in understanding the mathematical beauty of finite networks involved in many real-world applications.’

Yilun Shang Source: zbMATH

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The Mathematics of Finite Networks

An Introduction to Operator Graph Theory

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-viii

Preface
pp ix-xii

1 - Introduction
pp 1-10

Part I - Operator Graph Theory
pp 11-12

2 - Classical Graph Theory: The Mathematical Description of Networks
pp 13-87

3 - Operator Calculus: The Mapping between Vector Spaces
pp 88-116

4 - Operator Graph Theory: The Mathematics of Finite Networks
pp 117-178

Part II - Applications
pp 179-180

5 - Generating Graphs
pp 181-237

6 - Measuring Graphs
pp 238-290

7 - Transforming Graphs
pp 291-324

Afterthought
pp 325-326

Bibliography
pp 327-332

Index of Notations
pp 333-335

Subject Index
pp 336-342

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The Mathematics of Finite Networks

An Introduction to Operator Graph Theory

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