## Towards an Information Theory of Complex Networks: Statistical Methods and ApplicationsMatthias Dehmer, Frank Emmert-Streib, Alexander Mehler 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, 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

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 |