Quantitative Graph Theory by Dehmer, Matthias; Emmert-Streib, Frank;

Short description:

This is the first book devoted exclusively to quantitative graph theory. It presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs. Through its broad coverage, this text fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines.

Long description:

The first book devoted exclusively to quantitative graph theory, Quantitative Graph Theory: Mathematical Foundations and Applications presents and demonstrates existing and novel methods for analyzing graphs quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, this book covers a wide range of quantitative-graph theoretical concepts and methods, including those pertaining to real and random graphs such as:

• Comparative approaches (graph similarity or distance)



• Graph measures to characterize graphs quantitatively



• Applications of graph measures in social network analysis and other disciplines



• Metrical properties of graphs and measures



• Mathematical properties of quantitative methods or measures in graph theory



• Network complexity measures and other topological indices



• Quantitative approaches to graphs using machine learning (e.g., clustering)



• Graph measures and statistics



• Information-theoretic methods to analyze graphs quantitatively (e.g., entropy)

Through its broad coverage, Quantitative Graph Theory: Mathematical Foundations and Applications fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines. It is intended for researchers as well as graduate and advanced undergraduate students in the fields of mathematics, computer science, mathematical chemistry, cheminformatics, physics, bioinformatics, and systems biology.

Table of Contents:

What Is Quantitative Graph Theory?. Localization of Graph Topological Indices via Majorization Technique. Wiener Index of Hexagonal Chains with Segments of Equal Length. Metric-Extremal Graphs. Quantitative Methods for Nowhere-Zero Flows and Edge Colorings. Width-Measures for Directed Graphs and Algorithmic Applications. Betweenness Centrality in Graphs. On a Variant Szeged and PI Indices of Thorn Graphs. Wiener Index of Line Graphs. Single-Graph Support Measures. Network Sampling Algorithms and Applications. Discrimination of Image Textures Using Graph Indices. Network Analysis Applied to the Political Networks of Mexico. Social Network Centrality, Movement Identification, and the Participation of Individuals in a Social Movement: The Case of the Canadian Environmental Movement. Graph Kernels in Chemoinformatics. Chemical Compound Complexity in Biological Pathways.