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Author: Maarten van Steen
Publisher: Maarten Van Steen
ISBN: 9789081540612
Category : Graph theory
Languages : en
Pages : 285
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Book Description
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.
Author: Maarten van Steen
Publisher: Maarten Van Steen
ISBN: 9789081540612
Category : Graph theory
Languages : en
Pages : 285
Get Book Here
Book Description
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.
Author: Piet van Mieghem
Publisher: Cambridge University Press
ISBN: 1139492276
Category : Technology & Engineering
Languages : en
Pages : 363
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Book Description
Analyzing the behavior of complex networks is an important element in the design of new man-made structures such as communication systems and biologically engineered molecules. Because any complex network can be represented by a graph, and therefore in turn by a matrix, graph theory has become a powerful tool in the investigation of network performance. This self-contained 2010 book provides a concise introduction to the theory of graph spectra and its applications to the study of complex networks. Covering a range of types of graphs and topics important to the analysis of complex systems, this guide provides the mathematical foundation needed to understand and apply spectral insight to real-world systems. In particular, the general properties of both the adjacency and Laplacian spectrum of graphs are derived and applied to complex networks. An ideal resource for researchers and students in communications networking as well as in physics and mathematics.
Author: Vito Latora
Publisher: Cambridge University Press
ISBN: 1108298680
Category : Science
Languages : en
Pages : 585
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Book Description
Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems and metabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. Rigorous and thorough, this textbook presents a detailed overview of the new theory and methods of network science. Covering algorithms for graph exploration, node ranking and network generation, among others, the book allows students to experiment with network models and real-world data sets, providing them with a deep understanding of the basics of network theory and its practical applications. Systems of growing complexity are examined in detail, challenging students to increase their level of skill. An engaging presentation of the important principles of network science makes this the perfect reference for researchers and undergraduate and graduate students in physics, mathematics, engineering, biology, neuroscience and the social sciences.
Author: Matthias Dehmer
Publisher: Springer Science & Business Media
ISBN: 0817647899
Category : Mathematics
Languages : en
Pages : 493
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Book Description
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.
Author: Fan R. K. Chung
Publisher: American Mathematical Soc.
ISBN: 0821836579
Category : Computers
Languages : en
Pages : 274
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Book Description
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: Ernesto Estrada
Publisher: Oxford University Press
ISBN: 019959175X
Category : Computers
Languages : en
Pages : 478
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Book Description
The book integrates approaches from mathematics, physics and computer sciences to analyse the organisation of complex networks. Every organisational principle of networks is defined, quantified and then analysed for its influences on the properties and functions of molecular, biological, ecological and social networks.
Author: Albert-László Barabási
Publisher: Cambridge University Press
ISBN: 1107076269
Category : Computers
Languages : en
Pages : 477
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Book Description
Illustrated throughout in full colour, this pioneering text is the only book you need for an introduction to network science.
Author: Ravindra B. Bapat
Publisher: Springer
ISBN: 1447165691
Category : Mathematics
Languages : en
Pages : 197
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Book Description
This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.
Author: Chai Wah Wu
Publisher: World Scientific
ISBN: 9812709746
Category : Mathematics
Languages : en
Pages : 168
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Book Description
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
Author: Stefan Bornholdt
Publisher: John Wiley & Sons
ISBN: 3527606335
Category : Science
Languages : en
Pages : 417
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Book Description
Complex interacting networks are observed in systems from such diverse areas as physics, biology, economics, ecology, and computer science. For example, economic or social interactions often organize themselves in complex network structures. Similar phenomena are observed in traffic flow and in communication networks as the internet. In current problems of the Biosciences, prominent examples are protein networks in the living cell, as well as molecular networks in the genome. On larger scales one finds networks of cells as in neural networks, up to the scale of organisms in ecological food webs. This book defines the field of complex interacting networks in its infancy and presents the dynamics of networks and their structure as a key concept across disciplines. The contributions present common underlying principles of network dynamics and their theoretical description and are of interest to specialists as well as to the non-specialized reader looking for an introduction to this new exciting field. Theoretical concepts include modeling networks as dynamical systems with numerical methods and new graph theoretical methods, but also focus on networks that change their topology as in morphogenesis and self-organization. The authors offer concepts to model network structures and dynamics, focussing on approaches applicable across disciplines.
