Towards an Information Theory of Complex Networks: Statistical Methods and Applications

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Matthias Dehmer, Frank Emmert-Streib, Alexander Mehler
Springer Science & Business Media, Aug 26, 2011 - Mathematics - 395 pages

For over a decade, complex networks have steadily grown as an important tool across a broad array of academic disciplines, with applications ranging from physics to social media. A tightly organized collection of carefully-selected papers on the subject, Towards an Information Theory of Complex Networks: Statistical Methods and Applications presents theoretical and practical results about information-theoretic and statistical models of complex networks in the natural sciences and humanities. The book's major goal is to advocate and promote a combination of graph-theoretic, information-theoretic, and statistical methods as a way to better understand and characterize real-world networks.

This volume is the first to present a self-contained, comprehensive overview of information-theoretic models of complex networks with an emphasis on applications. As such, it marks a first step toward establishing advanced statistical information theory as a unified theoretical basis of complex networks for all scientific disciplines and can serve as a valuable resource for a diverse audience of advanced students and professional scientists. While it is primarily intended as a reference for research, the book could also be a useful supplemental graduate text in courses related to information science, graph theory, machine learning, and computational biology, among others.

 

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Contents

Chapter 1 Entropy of Digraphs and Infinite Networks
1
Chapter 2 An InformationTheoretic Upper Bound on Planar Graphs Using WellOrderly Maps
17
Chapter 3 Probabilistic Inference Using Function Factorization and Divergence Minimization
47
Chapter 4 Wave Localization on Complex Networks
75
Chapter 5 InformationTheoretic Methods in Chemical Graph Theory
97
Chapter 6 On the Development and Application of NetSign Graph Theory
127
Chapter 7 The Central Role of Information Theory in Ecology
153
Chapter 8 Inferences About Coupling from Ecological Surveillance Monitoring Approaches Based on Nonlinear Dynamics and Information Theory
168
Chapter 9 Markov Entropy Centrality Chemical Biological Crime and Legislative Networks
199
Chapter 10 Social Ontologies as Generalized Nearly Acyclic Directed Graphs A Quantitative Graph Model of Social Tagging
259
Chapter 11 Typology by Means of Language Networks Applying Information Theoretic Measures to Morphological Derivation Networks
321
Chapter 12 Information TheoryBased Measurement of Software
347
Chapter 13 Fair and Biased Random Walks on Undirected Graphs and Related Entropies
365
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