Structural Analysis of Complex Networks - Dehmer, Matthias; SpringerLink (Online service) (Boston : Birkhäuser Boston, 2011)
Because of the increasing complexity and growth of real-world networks, their analysis by using classical graph-theoretic methods is oftentimes a difficult procedure. As a result, there is a strong need to combine graph-theoretic methods with mathematical techniques from other scientific disciplines, such as machine learning and information theory, in order to analyze complex networks more adequately. Filling a gap in literature, this self-contained book presents theoretical and application-oriented results to structurally explore complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Special emphasis is given to methods related to the following areas: * Applications to biology, chemistry, linguistics, and data analysis * Graph colorings * Graph polynomials * Information measures for graphs * Metrical properties of graphs * Partitions and decompositions * Quantitative graph measures Structural Analysis of Complex Networks is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. The book may be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.
Preface -- A Brief Introduction to Complex Networks and Their Analysis -- Partitions of Graphs -- Distance in Graphs -- Domination in Graphs -- Spectrum and Entropy for Infinite Directed Graphs -- Application of Infinite Labeled Graphs to Symbolic Dynamical Systems -- Decompositions and Factorizations of Complete Graphs -- Geodetic Sets in Graphs -- Graph Polynomials and Their Applications I: The Tutte Polynomial -- Graph Polynomials and Their Applications II: Interrelations and Interpretations -- Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations -- Subgraphs as a Measure of Similarity -- A Chromatic Metric on Graphs -- Some Applications of Eigenvalues of Graphs -- Minimum Spanning Markovian Trees: Introducing Context-Sensitivity Into the Generation of Spanning Trees -- Link-Based Network Mining -- Graph Representations and Algorithms in Computational Biology of RNA Secondary Structure -- Inference of Protein Function from the Structure of Interaction Networks -- Applications of Perfect Matchings in Chemistry -- Index.
Keywords: Mathematics; Computer Communication Networks; Computational complexity; Data mining; Bioinformatics; Combinatorics; Mathematics; Applications of Mathematics; Discrete Mathematics in Computer Science; Combinatorics; Computer Communication Networks; Computational Biology/Bioinformatics.; Data Mining and Knowledge Discovery