Ebook: Structural Analysis of Complex Networks
- Tags: Applications of Mathematics, Discrete Mathematics in Computer Science, Combinatorics, Computer Communication Networks, Computational Biology/Bioinformatics, Data Mining and Knowledge Discovery
- Year: 2011
- Publisher: Birkhäuser Basel
- Edition: 1
- Language: English
- pdf
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.
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.
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.
Content:
Front Matter....Pages i-xiii
A Brief Introduction to Complex Networks and Their Analysis....Pages 1-26
Partitions of Graphs....Pages 27-47
Distance in Graphs....Pages 49-72
Domination in Graphs....Pages 73-104
Spectrum and Entropy for Infinite Directed Graphs....Pages 105-136
Application of Infinite Labeled Graphs to Symbolic Dynamical Systems....Pages 137-168
Decompositions and Factorizations of Complete Graphs....Pages 169-196
Geodetic Sets in Graphs....Pages 197-218
Graph Polynomials and Their Applications I: The Tutte Polynomial....Pages 219-255
Graph Polynomials and Their Applications II: Interrelations and Interpretations....Pages 257-292
Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations....Pages 293-317
Subgraphs as a Measure of Similarity....Pages 319-334
A Chromatic Metric on Graphs....Pages 335-356
Some Applications of Eigenvalues of Graphs....Pages 357-379
Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees....Pages 381-401
Link-Based Network Mining....Pages 403-419
Graph Representations and Algorithms in Computational Biology of RNA Secondary Structure....Pages 421-437
Inference of Protein Function from the Structure of Interaction Networks....Pages 439-461
Applications of Perfect Matchings in Chemistry....Pages 463-482
Back Matter....Pages 483-486
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.
Content:
Front Matter....Pages i-xiii
A Brief Introduction to Complex Networks and Their Analysis....Pages 1-26
Partitions of Graphs....Pages 27-47
Distance in Graphs....Pages 49-72
Domination in Graphs....Pages 73-104
Spectrum and Entropy for Infinite Directed Graphs....Pages 105-136
Application of Infinite Labeled Graphs to Symbolic Dynamical Systems....Pages 137-168
Decompositions and Factorizations of Complete Graphs....Pages 169-196
Geodetic Sets in Graphs....Pages 197-218
Graph Polynomials and Their Applications I: The Tutte Polynomial....Pages 219-255
Graph Polynomials and Their Applications II: Interrelations and Interpretations....Pages 257-292
Reconstruction Problems for Graphs, Krawtchouk Polynomials, and Diophantine Equations....Pages 293-317
Subgraphs as a Measure of Similarity....Pages 319-334
A Chromatic Metric on Graphs....Pages 335-356
Some Applications of Eigenvalues of Graphs....Pages 357-379
Minimum Spanning Markovian Trees: Introducing Context-Sensitivity into the Generation of Spanning Trees....Pages 381-401
Link-Based Network Mining....Pages 403-419
Graph Representations and Algorithms in Computational Biology of RNA Secondary Structure....Pages 421-437
Inference of Protein Function from the Structure of Interaction Networks....Pages 439-461
Applications of Perfect Matchings in Chemistry....Pages 463-482
Back Matter....Pages 483-486
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