A First Course in Network Theory

A First Course in Network Theory

A First Course in Network Theory

A First Course in Network Theory

Synopsis

The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and sociology. This book promotes the diverse nature of the study of complex networks by balancing the needs of students from very different backgrounds. It references the most commonly used concepts in network theory, provides examples of their applications in solving practical problems, and clear indications on how to analyse their results. In the first part of the book, students and researchers will discover the quantitative and analytical tools necessary to work with complex networks, including the most basic concepts in network and graph theory, linear and matrix algebra, as well as the physical concepts most frequently used for studying networks. They will also find instruction on some key skills such as how to proof analytic results and how to manipulate empirical network data. The bulk of the text is focused on instructing readers on the most useful tools for modern practitioners of network theory. These include degree distributions, random networks, network fragments, centrality measures, clusters and communities, communicability, and local and global properties of networks. The combination of theory, example and method that are presented in this text, should ready the student to conduct their own analysis of networks with confidence and allow teachers to select appropriate examples and problems to teach this subject in the classroom.

Excerpt

The origins of this book can be traced to lecture notes we prepared for a class entitled Introduction to Network Theory offered by the Department of Mathematics and Statistics at the University of Strathclyde and attended by undergraduate students in the Honour courses in the department. the course has since been extended, based on experience gained in teaching the course to graduate students and postdoctoral researchers from a variety of backgrounds around the world. To mathematicians, physicists, and computer scientists at Emory University in Atlanta. To postgraduate students in biological and environmental sciences on courses sponsored by the Natural Environmental Research Council in the UK. To Masters students on intensive short courses at the African Institute of Mathematical Sciences in both South Africa and Ghana. and to mathematicians, computer scientists, physicists, and more at an International Summer School on Complex Networks in Bertinoro, Italy.

Designing courses with a common thread suitable for students with very different backgrounds represents a big challenge. For example, the balance between theory and application will vary significantly between students of mathematics and students of computer sciences. An even greater challenge is to ensure that those students with an interest in network theory, but who lack the normal quantitative backgrounds expected on a mathematics course, do not become frustrated by being overloaded by seemingly unnecessary theory. We believe in the interdisciplinary nature of the study of complex networks. the aim of this book is to approach our students in an interdisciplinary fashion and as a consequence we try to avoid a heavy mathematical bias. We have avoided a didactic ‘Theorem– Proof’ approach but we do not believe we have sacrificed rigour and the book is replete with examples and solved problems which will lead students through the theory as constructively as possible.

This book is written with senior undergraduate students and new graduate students in mind. the major prerequisite is elementary algebra at a level one would expect in the first year of an undergraduate science degree. To make this book accessible for students from non-quantitative subjects we explain most of the basic concepts of linear algebra needed to understand the more specific topics of network theory. This material should not be wasted on students coming from more quantitative subjects. As well as providing a reminder of familiar concepts, we expect they will encounter a number of simple results which are not typically presented in undergraduate linear algebra courses. We insist on no prerequisites in graph theory for understanding this book since we believe it contains all the necessary basic concepts in that area to allow progress in network theory. Based . . .

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