Applying Graph Theory In Ecological Research

This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.

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

Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.

Ecology is one of the most challenging of sciences, with unambiguous knowledge much harder to achieve than it might seem. But it is also one of the most important sciences for the future health of our planet. It is vital that our efforts are as effective as possible at achieving our desired outcomes. This book is intended to help individual ecologists to develop a better vision for their ecology – and the way they can best contribute to science. The central premise is that to advance ecology effectively as a discipline, ecologists need to be able to establish conclusive answers to key questions rather than merely proposing plausible explanations for mundane observations. Ecologists need clear and honest understanding of how we have come to do things the way we do them now, the limitations of our approaches, our goals for the future and how we may need to change our approaches if we are to maintain or enhance our relevance and credibility. Readers are taken through examples to show what a critical appraisal can reveal and how this approach can benefit ecology if it is applied more routinely. Ecological systems are notable for their complexity and their variability. Ecology is, as indicated by the title of this book, a truly difficult science. Ecologists have achieved a great deal, but they can do better. This book aims to encourage early-career researchers to be realistic about their expectations: to question everything, not to take everything for granted, and to make up their own minds.

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.

This research monograph provides the means to learn the theory and practice of graph and network analysis using the Python programming language. The social network analysis techniques, included, will help readers to efficiently analyze social data from Twitter, Facebook, LiveJournal, GitHub and many others at three levels of depth: ego, group, and community. They will be able to analyse militant and revolutionary networks and candidate networks during elections. For instance, they will learn how the Ebola virus spread through communities. Practically, the book is suitable for courses on social network analysis in all disciplines that use social methodology. In the study of social networks, social network analysis makes an interesting interdisciplinary research area, where computer scientists and sociologists bring their competence to a level that will enable them to meet the challenges of this fast-developing field. Computer scientists have the knowledge to parse and process data while sociologists have the experience that is required for efficient data editing and interpretation. Social network analysis has successfully been applied in different fields such as health, cyber security, business, animal social networks, information retrieval, and communications.

This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.

A review and evaluation of the analysis methods for studying spatial pattern in vegetation.