The mathematics of finite networks : an introduction to operator graph theory / Michael Rudolph.

Format:

Book

Author/Creator:

Rudolph, Michael, 1969- author.

Language:

English

Subjects (All):

Graph theory.

Operator theory.

System analysis.

Physical Description:

1 online resource (xii, 342 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge ; New York, NY : Cambridge University Press, 2022.

Summary:

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.

Contents:

Classical graph theory

Operator calculus

Operator graph theory

Generating graphs

Measuring graphs

Transforming graphs.

Notes:

Title from publisher's bibliographic system (viewed on 07 Apr 2022).

Includes bibliographical references.

ISBN:

1-009-28783-4

1-316-46691-4