Graph Theory and Complex Networks

Graph Theory and Complex Networks PDF 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.

Graph Theory and Complex Networks

Graph Theory and Complex Networks PDF 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.

Graph Spectra for Complex Networks

Graph Spectra for Complex Networks PDF 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.

Complex Networks

Complex Networks PDF Author: Kayhan Erciyes
Publisher: CRC Press
ISBN: 1466571675
Category : Computers
Languages : en
Pages : 318

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Book Description
Complex Networks: An Algorithmic Perspective supplies the basic theoretical algorithmic and graph theoretic knowledge needed by every researcher and student of complex networks. This book is about specifying, classifying, designing, and implementing mostly sequential and also parallel and distributed algorithms that can be used to analyze the static properties of complex networks. Providing a focused scope which consists of graph theory and algorithms for complex networks, the book identifies and describes a repertoire of algorithms that may be useful for any complex network.

Structural Analysis of Complex Networks

Structural Analysis of Complex Networks PDF 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.

The Structure of Complex Networks

The Structure of Complex Networks PDF 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.

Complex Graphs and Networks

Complex Graphs and Networks PDF 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.

Network Science

Network Science PDF 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.

Synchronization in Complex Networks of Nonlinear Dynamical Systems

Synchronization in Complex Networks of Nonlinear Dynamical Systems PDF 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.

Algorithmic Graph Theory

Algorithmic Graph Theory PDF Author: Alan Gibbons
Publisher: Cambridge University Press
ISBN: 9780521288811
Category : Computers
Languages : en
Pages : 280

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Book Description
An introduction to pure and applied graph theory with an emphasis on algorithms and their complexity.

Handbook of Graphs and Networks

Handbook of Graphs and Networks PDF 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.