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The Mathematics of Finite Networks - An Introduction to Operator Graph Theory (Hardcover)
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The Mathematics of Finite Networks - An Introduction to Operator Graph Theory (Hardcover)
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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.
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