Quantitative Graph Theory

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 technique

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.

Building on the background of graph theory provided in the first volume of the series, presents a detailed examination of the role of graph theory in the study of chemical kinetics, reaction mechanisms, and quantitative structure-activity relations, in a manner useful to theoretical chemists. Among the topics are heterogeneous catalytic reactions, the classification and coding of chemical reaction mechanisms, the mechanist's description of chemical processes as it relates to aromaticity, and using operator networks to interpret evolutionary interrelations between chemical entities. Annotation copyright by Book News, Inc., Portland, OR

This latest addition to the successful Network Biology series presents current methods for determining the entropy of networks, making it the first to cover the recently established Quantitative Graph Theory. An excellent international team of editors and contributors provides an up-to-date outlook for the field, covering a broad range of graph entropy-related concepts and methods. The topics range from analyzing mathematical properties of methods right up to applying them in real-life areas. Filling a gap in the contemporary literature this is an invaluable reference for a number of disciplines, including mathematicians, computer scientists, computational biologists, and structural chemists.

Modern medicine is undergoing a paradigm shift from a "one-size-fits-all" strategy to a more precise patient-customized therapy and medication plan. While the success of precision medicine relies on the level of pharmacogenomic knowledge, dissecting the genetic mechanisms of drug response in a sufficient detail requires powerful computational tools. Quantitative Methods for Precision Medicine: Pharmacogenomics in Action presents the advanced statistical methods for mapping pharmacogenetic control by integrating pharmacokinetic and pharmacodynamic principles of drug-body interactions. Beyond traditional reductionist-based statistical genetic approaches, statistical formulization in this book synthesizes elements of multiple disciplines to infer, visualize, and track how pharmacogenes interact together as an intricate but well-coordinated system to mediate patient-specific drug response. Features: Functional and systems mapping models to characterize the genetic architecture of multiple medication processes Statistical methods for analyzing informative missing data in pharmacogenetic association studies Functional graph theory of inferring genetic interaction networks from association data Leveraging the concept of epistasis to capture its bidirectional, signed and weighted properties Modeling gene-induced cell-cell crosstalk and its impact on drug response A graph model of drug-drug interactions in combination therapies Critical methodological issues to improve pharmacogenomic research as the cornerstone of precision medicine This book is suitable for graduate students and researchers in the fields of biology, medicine, bioinformatics and drug design and delivery who are interested in statistical and computational modelling of biological processes and systems. It may also serve as a major reference for applied mathematicians, computer scientists, and statisticians who attempt to develop algorithmic tools for genetic mapping, systems pharmacogenomics and systems biology. It can be used as both a textbook and research reference. Professionals in pharmaceutical sectors who design drugs and clinical doctors who deliver drugs will also find it useful.

Filling a gap in literature, this self-contained book presents theoretical and application-oriented results that allow for a structural exploration of complex networks. The work focuses not only on classical graph-theoretic methods, but also demonstrates the usefulness of structural graph theory as a tool for solving interdisciplinary problems. Applications to biology, chemistry, linguistics, and data analysis are emphasized. The book is suitable for a broad, interdisciplinary readership of researchers, practitioners, and graduate students in discrete mathematics, statistics, computer science, machine learning, artificial intelligence, computational and systems biology, cognitive science, computational linguistics, and mathematical chemistry. It may also be used as a supplementary textbook in graduate-level seminars on structural graph analysis, complex networks, or network-based machine learning methods.

Displays the broad range of quantitative approaches to analysing ecological networks, providing clear examples and guidance for researchers.

This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated, algebraic statements of social and political phenomena.