Random Graphs And Networks A First Course
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Author | : Alan Frieze |
Publisher | : Cambridge University Press |
Total Pages | : 233 |
Release | : 2023-03-31 |
Genre | : Computers |
ISBN | : 1009260286 |
A rigorous yet accessible introduction to the rapidly expanding subject of random graphs and networks.
Author | : Alan Frieze |
Publisher | : Cambridge University Press |
Total Pages | : 483 |
Release | : 2016 |
Genre | : Mathematics |
ISBN | : 1107118506 |
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author | : Remco van der Hofstad |
Publisher | : Cambridge University Press |
Total Pages | : 341 |
Release | : 2017 |
Genre | : Computers |
ISBN | : 110717287X |
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author | : Alan Frieze |
Publisher | : Cambridge University Press |
Total Pages | : 234 |
Release | : 2023-03-09 |
Genre | : Mathematics |
ISBN | : 1009260316 |
Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.
Author | : Rick Durrett |
Publisher | : Cambridge University Press |
Total Pages | : 203 |
Release | : 2010-05-31 |
Genre | : Mathematics |
ISBN | : 1139460889 |
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author | : Ernesto Estrada |
Publisher | : Oxford University Press, USA |
Total Pages | : 269 |
Release | : 2015 |
Genre | : Science |
ISBN | : 0198726457 |
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.
Author | : Bela Bollobas |
Publisher | : Springer Science & Business Media |
Total Pages | : 191 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461299675 |
From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1
Author | : Anthony C. C. Coolen |
Publisher | : Oxford University Press |
Total Pages | : 325 |
Release | : 2017 |
Genre | : Computers |
ISBN | : 0198709897 |
This book describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'.
Author | : Fan R. K. Chung |
Publisher | : American Mathematical Soc. |
Total Pages | : 274 |
Release | : 2006 |
Genre | : Computers |
ISBN | : 0821836579 |
Graph theory is a primary tool for detecting numerous hidden structures in various information networks, including Internet graphs, social networks, biological networks, or any graph representing relations in massive data sets. This book explains the universal and ubiquitous coherence in the structure of these realistic but complex networks.
Author | : Maarten van Steen |
Publisher | : Maarten Van Steen |
Total Pages | : 285 |
Release | : 2010 |
Genre | : Graph theory |
ISBN | : 9789081540612 |
This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science. Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks. In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they: 1.Have learned how to read and understand the basic mathematics related to graph theory. 2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks. 3.Know a bit more about this sometimes mystical field of small worlds and random networks. There is an accompanying web site www.distributed-systems.net/gtcn from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks.