Quantitative Graph Theory: Mathematical Foundations and Applications

Content: Preface Editors Contributors 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, Jose 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 Coronicova Hurajova, and Tomas 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 Skrekovski 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; Benoit Gauzere, Luc Brun, and Didier Villemin Chemical Compound Complexity in Biological Pathways; Atsuko Yamaguchi and Kiyoko F. Aoki-Kinoshita Index
Abstract: ''This book presents methods for analyzing graphs and networks quantitatively. Incorporating interdisciplinary knowledge from graph theory, information theory, measurement theory, and statistical techniques, it covers a wide range of quantitative graph-theoretical concepts and methods, including those pertaining to random graphs. Through its broad coverage, the book fills a gap in the contemporary literature of discrete and applied mathematics, computer science, systems biology, and related disciplines''--

''Graph-based approaches have been employed extensively in several disciplines such as biology, computer science, chemistry, and so forth. In the 1990s, exploration of the topology of complex networks became quite popular and was triggered by the breakthrough of the Internet and the examinations of random networks. As a consequence, the structure of random networks has been explored using graph-theoretic methods and stochastic growth models. However, it turned out that besides exploring random graphs, quantitative approaches to analyze networks are crucial as well. This relates to quantifying structural information of complex networks by using ameasurement approach. As demonstrated in the scientific literature, graph- and informationtheoretic measures, and statistical techniques applied to networks have been used to do this quantification. It has been found that many real-world networks are composed of network patterns representing nonrandom topologies.Graph- and information-theoretic measures have been proven efficient in quantifying the structural information of such patterns. The study of relevant literature reveals that quantitative graph theory has not yet been considered a branch of graph theory''