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:
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.
"… includes some papers with particular emphasis in the applications of quantitative graph theory. … It is always very nice when we learn of such varied applications of mathematics in general and graph theory in particular. Most of the chapters should be accessible to graduate students. Some of them also include quite a large bibliography for further reference. … this book fills indeed a gap in the discrete mathematics literature and is going to improve the status of quantitative graph theory."
—Zentralblatt MATH 1310
"The editors have done a nice job collecting articles that will be accessible to most graduate students in mathematics. … these articles will give an interesting taste of some exciting mathematics and give the reader plenty of ideas of where to go to learn more. If nothing else, this collection will convince readers that graph theory, or at least large parts of it, belongs solidly under the category of applied mathematics, and that there is very interesting work being done in the area."
—Darren Glass, MAA Reviews, January 2015
What Is Quantitative Graph Theory?; Matthias Dehmer, Veronika Kraus, Frank Emmert-Streib, and Stefan Pickl
Localization of Graph Topological Indices via Majorization Technique; Monica Bianchi, Alessandra Cornaro, José Luis Palacios, and Anna Torriero
Wiener Index of Hexagonal Chains with Segments of Equal Length; Andrey A. Dobrynin
Metric-Extremal Graphs; Ivan Gutman and Boris Furtula
Quantitative Methods for Nowhere-Zero Flows and Edge Colorings; Martin Kochol
Width-Measures for Directed Graphs and Algorithmic Applications; Stephan Kreutzer and Sebastian Ordyniak
Betweenness Centrality in Graphs; Silvia Gago, Jana Coroniˇcová Hurajová, and Tomáš Madaras
On a Variant Szeged and PI Indices of Thorn Graphs; Mojgan Mogharrab and Reza Sharafdini
Wiener Index of Line Graphs; Martin Knor and Riste Škrekovski
Single-Graph Support Measures; Toon Calders, Jan Ramon, and Dries Van Dyck
Network Sampling Algorithms and Applications; Michael Drew LaMar and Rex K. Kincaid
Discrimination of Image Textures Using Graph Indices; Martin Welk
Network Analysis Applied to the Political Networks of Mexico; Philip A. Sinclair
Social Network Centrality, Movement Identification, and the Participation of Individuals in a Social Movement: The Case of the Canadian Environmental Movement; David B. Tindall, Joanna L. Robinson, and Mark C.J. Stoddart
Graph Kernels in Chemoinformatics; Benoît Gaüzère, Luc Brun, and Didier Villemin
Chemical Compound Complexity in Biological Pathways; Atsuko Yamaguchi and Kiyoko F. Aoki-Kinoshita