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Introduction to the Theory of Complex Systems$
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Stefan Thurner, Peter Klimek, and Rudolf Hanel

Print publication date: 2018

Print ISBN-13: 9780198821939

Published to Oxford Scholarship Online: November 2018

DOI: 10.1093/oso/9780198821939.001.0001

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(p.140) 4 Networks
Introduction to the Theory of Complex Systems

Stefan Thurner

Rudolf Hanel

Peter Klimekl

Oxford University Press

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

Keywords:   Random walk on networks, small-world network, eigenvalue spectra, community detection, correlation networks, diffusion on networks, network centrality, generalized networks, multilayer networks, systemic risk

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