Quantitative Graph Theory: Mathematical Foundations and Applications, 1st Edition (Hardback) book cover

Quantitative Graph Theory

Mathematical Foundations and Applications, 1st Edition

Edited by Matthias Dehmer, Frank Emmert-Streib

Chapman and Hall/CRC

528 pages | 268 B/W Illus.

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Hardback: 9781466584518
pub: 2014-10-27
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pub: 2014-10-27
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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.


"… 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

Table of Contents




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


About the Editors

Matthias Dehmer studied mathematics and computer science at the University of Siegen, Germany, and earned his Ph.D in computer science from the Darmstadt University of Technology. He held research positions at the University of Rostock (Germany), Vienna Bio Center (Austria), Vienna Technical University (Austria), and University of Coimbra (Portugal), and obtained his habilitation in applied discrete mathematics from the Vienna University of Technology. His research focuses on investigating network-based methods in the context of systems biology, structural graph theory, operations research, and information theory. He has over 180 peer-reviewed publications, is an editor of a book series and a member of multiple editorial boards, and has co/organized several scientific conferences.

Frank Emmert-Streib studied physics at the University of Siegen, Germany, and earned his Ph.D in theoretical physics from the University of Bremen. After postdoc positions in the United States, he joined the Center for Cancer Research and Cell Biology at the Queen’s University Belfast (United Kingdom), where he is currently an associate professor (senior lecturer) leading the Computational Biology and Machine Learning Laboratory. His research interests are in the fields of computational biology, biostatistics, and network medicine and are focused on the development and application of methods from statistics and machine learning for the analysis of high-dimensional data from genomics experiments.

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Operating Systems / General
MATHEMATICS / Combinatorics
SCIENCE / Life Sciences / Biology / General