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