[PDF] Graph Theory And Complex Networks eBook

Author : Maarten van Steen
Publisher : Maarten Van Steen
Page : 285 pages
File Size : 23,15 MB
Release : 2010
Category : Graph theory
ISBN : 9789081540612

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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
Page : 363 pages
File Size : 12,62 MB
Release : 2010-12-02
Category : Technology & Engineering
ISBN : 1139492276

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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 : Albert-László Barabási
Publisher : Cambridge University Press
Page : 477 pages
File Size : 43,37 MB
Release : 2016-07-21
Category : Computers
ISBN : 1107076269

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Illustrated throughout in full colour, this pioneering text is the only book you need for an introduction to network science.

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 28,84 MB
Release : 2017
Category : Computers
ISBN : 110717287X

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This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.

Author : Vito Latora
Publisher : Cambridge University Press
Page : 585 pages
File Size : 29,42 MB
Release : 2017-09-28
Category : Science
ISBN : 1108298680

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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
Page : 493 pages
File Size : 22,55 MB
Release : 2010-10-14
Category : Mathematics
ISBN : 0817647899

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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.
Page : 274 pages
File Size : 22,90 MB
Release : 2006
Category : Computers
ISBN : 0821836579

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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
Page : 478 pages
File Size : 44,75 MB
Release : 2012
Category : Computers
ISBN : 019959175X

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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 : Matthias Dehmer
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 34,15 MB
Release : 2009-07-10
Category : Medical
ISBN : 3527627995

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Mathematical problems such as graph theory problems are of increasing importance for the analysis of modelling data in biomedical research such as in systems biology, neuronal network modelling etc. This book follows a new approach of including graph theory from a mathematical perspective with specific applications of graph theory in biomedical and computational sciences. The book is written by renowned experts in the field and offers valuable background information for a wide audience.

Author : Stefan Bornholdt
Publisher : John Wiley & Sons
Page : 417 pages
File Size : 13,52 MB
Release : 2006-03-06
Category : Science
ISBN : 3527606335

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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.