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  1. Home
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  3. The Mathematics of Finite Networks
  • Cited by 1
  • 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
Information

Book description

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.

Reviews

‘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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