Graph Theory And Complex Networks

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Graph Theory and Complex Networks

Maarten van Steen
Graph Theory and Complex Networks Book PDF

Author : Maarten van Steen
Publisher : Maarten Van Steen
Page : 285 pages
File Size : 50,5 Mb
Release : 2010
Category : Graph theory
ISBN : 9081540610

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Graph Theory and Complex Networks by Maarten van Steen Pdf

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

Piet van Mieghem
Graph Spectra for Complex Networks Book PDF

Author : Piet van Mieghem
Publisher : Cambridge University Press
Page : 363 pages
File Size : 49,5 Mb
Release : 2010-12-02
Category : Technology & Engineering
ISBN : 9781139492270

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Graph Spectra for Complex Networks by Piet van Mieghem Pdf

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.

Mining Complex Networks

Bogumil Kaminski,Pawel Prałat,Francois Theberge
Mining Complex Networks Book PDF

Author : Bogumil Kaminski,Pawel Prałat,Francois Theberge
Publisher : CRC Press
Page : 278 pages
File Size : 50,7 Mb
Release : 2021-12-15
Category : Mathematics
ISBN : 9781000515855

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Mining Complex Networks by Bogumil Kaminski,Pawel Prałat,Francois Theberge Pdf

This book concentrates on mining networks, a subfield within data science. Data science uses scientific and computational tools to extract valuable knowledge from large data sets. Once data is processed and cleaned, it is analyzed and presented to support decision-making processes. Data science and machine learning tools have become widely used in companies of all sizes. Networks are often large-scale, decentralized, and evolve dynamically over time. Mining complex networks aim to understand the principles governing the organization and the behavior of such networks is crucial for a broad range of fields of study. Here are a few selected typical applications of mining networks: Community detection (which users on some social media platforms are close friends). Link prediction (who is likely to connect to whom on such platforms). Node attribute prediction (what advertisement should be shown to a given user of a particular platform to match their interests). Influential node detection (which social media users would be the best ambassadors of a specific product). This textbook is suitable for an upper-year undergraduate course or a graduate course in programs such as data science, mathematics, computer science, business, engineering, physics, statistics, and social science. This book can be successfully used by all enthusiasts of data science at various levels of sophistication to expand their knowledge or consider changing their career path. Jupiter notebooks (in Python and Julia) accompany the book and can be accessed on https://www.ryerson.ca/mining-complex-networks/. These not only contain all the experiments presented in the book, but also include additional material. Bogumił Kamiński is the Chairman of the Scientific Council for the Discipline of Economics and Finance at SGH Warsaw School of Economics. He is also an Adjunct Professor at the Data Science Laboratory at Ryerson University. Bogumił is an expert in applications of mathematical modeling to solving complex real-life problems. He is also a substantial open-source contributor to the development of the Julia language and its package ecosystem. Paweł Prałat is a Professor of Mathematics in Ryerson University, whose main research interests are in random graph theory, especially in modeling and mining complex networks. He is the Director of Fields-CQAM Lab on Computational Methods in Industrial Mathematics in The Fields Institute for Research in Mathematical Sciences and has pursued collaborations with various industry partners as well as the Government of Canada. He has written over 170 papers and three books with 130 plus collaborators. François Théberge holds a B.Sc. degree in applied mathematics from the University of Ottawa, a M.Sc. in telecommunications from INRS and a PhD in electrical engineering from McGill University. He has been employed by the Government of Canada since 1996 where he was involved in the creation of the data science team as well as the research group now known as the Tutte Institute for Mathematics and Computing. He also holds an adjunct professorial position in the Department of Mathematics and Statistics at the University of Ottawa. His current interests include relational-data mining and deep learning.

Structural Analysis of Complex Networks

Matthias Dehmer
Structural Analysis of Complex Networks Book PDF

Author : Matthias Dehmer
Publisher : Springer Science & Business Media
Page : 493 pages
File Size : 49,7 Mb
Release : 2010-10-14
Category : Mathematics
ISBN : 9780817647896

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Structural Analysis of Complex Networks by Matthias Dehmer Pdf

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.

Complex Graphs and Networks

Fan Chung,Fan R. K. Chung,Fan Chung Graham,Linyuan Lu,Professor of Resiratory Medicine Kian Fan Chung
Complex Graphs and Networks Book PDF

Author : Fan Chung,Fan R. K. Chung,Fan Chung Graham,Linyuan Lu,Professor of Resiratory Medicine Kian Fan Chung
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 53,9 Mb
Release : 2006
Category : Combinatorial analysis
ISBN : 9780821836576

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Complex Graphs and Networks by Fan Chung,Fan R. K. Chung,Fan Chung Graham,Linyuan Lu,Professor of Resiratory Medicine Kian Fan Chung Pdf

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.

Random Graphs and Complex Networks

Remco van der Hofstad
Random Graphs and Complex Networks Book PDF

Author : Remco van der Hofstad
Publisher : Cambridge University Press
Page : 341 pages
File Size : 52,5 Mb
Release : 2016-12-22
Category : Computers
ISBN : 9781107172876

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Random Graphs and Complex Networks by Remco van der Hofstad Pdf

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

Complex Networks

Kayhan Erciyes
Complex Networks Book PDF

Author : Kayhan Erciyes
Publisher : CRC Press
Page : 318 pages
File Size : 49,5 Mb
Release : 2014-09-06
Category : Computers
ISBN : 9781466571679

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Complex Networks by Kayhan Erciyes Pdf

Network science is a rapidly emerging field of study that encompasses mathematics, computer science, physics, and engineering. A key issue in the study of complex networks is to understand the collective behavior of the various elements of these networks.Although the results from graph theory have proven to be powerful in investigating the structur

The Structure of Complex Networks

Ernesto Estrada
The Structure of Complex Networks Book PDF

Author : Ernesto Estrada
Publisher : Oxford University Press
Page : 478 pages
File Size : 46,9 Mb
Release : 2012
Category : Computers
ISBN : 9780199591756

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The Structure of Complex Networks by Ernesto Estrada Pdf

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.

Fundamentals of Complex Networks

Guanrong Chen,Xiaofan Wang,Xiang Li
Fundamentals of Complex Networks Book PDF

Author : Guanrong Chen,Xiaofan Wang,Xiang Li
Publisher : John Wiley & Sons
Page : 384 pages
File Size : 47,6 Mb
Release : 2015-06-29
Category : Computers
ISBN : 9781118718117

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Fundamentals of Complex Networks by Guanrong Chen,Xiaofan Wang,Xiang Li Pdf

Complex networks such as the Internet, WWW, transportation networks, power grids, biological neural networks, and scientific cooperation networks of all kinds provide challenges for future technological development. • The first systematic presentation of dynamical evolving networks, with many up-to-date applications and homework projects to enhance study • The authors are all very active and well-known in the rapidly evolving field of complex networks • Complex networks are becoming an increasingly important area of research • Presented in a logical, constructive style, from basic through to complex, examining algorithms, through to construct networks and research challenges of the future

Synchronization in Complex Networks of Nonlinear Dynamical Systems

Chai Wah Wu
Synchronization in Complex Networks of Nonlinear Dynamical Systems Book PDF

Author : Chai Wah Wu
Publisher : World Scientific
Page : 168 pages
File Size : 40,7 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812709745

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Synchronization in Complex Networks of Nonlinear Dynamical Systems by Chai Wah Wu Pdf

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.

Graphs and Matrices

Ravindra B. Bapat
Graphs and Matrices Book PDF

Author : Ravindra B. Bapat
Publisher : Springer
Page : 193 pages
File Size : 44,7 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9781447165699

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Graphs and Matrices by Ravindra B. Bapat Pdf

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.

Network Analysis Literacy

Katharina A. Zweig
Network Analysis Literacy Book PDF

Author : Katharina A. Zweig
Publisher : Springer Science & Business Media
Page : 535 pages
File Size : 49,6 Mb
Release : 2016-10-26
Category : Computers
ISBN : 9783709107416

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Network Analysis Literacy by Katharina A. Zweig Pdf

This book presents a perspective of network analysis as a tool to find and quantify significant structures in the interaction patterns between different types of entities. Moreover, network analysis provides the basic means to relate these structures to properties of the entities. It has proven itself to be useful for the analysis of biological and social networks, but also for networks describing complex systems in economy, psychology, geography, and various other fields. Today, network analysis packages in the open-source platform R and other open-source software projects enable scientists from all fields to quickly apply network analytic methods to their data sets. Altogether, these applications offer such a wealth of network analytic methods that it can be overwhelming for someone just entering this field. This book provides a road map through this jungle of network analytic methods, offers advice on how to pick the best method for a given network analytic project, and how to avoid common pitfalls. It introduces the methods which are most often used to analyze complex networks, e.g., different global network measures, types of random graph models, centrality indices, and networks motifs. In addition to introducing these methods, the central focus is on network analysis literacy – the competence to decide when to use which of these methods for which type of question. Furthermore, the book intends to increase the reader's competence to read original literature on network analysis by providing a glossary and intensive translation of formal notation and mathematical symbols in everyday speech. Different aspects of network analysis literacy – understanding formal definitions, programming tasks, or the analysis of structural measures and their interpretation – are deepened in various exercises with provided solutions. This text is an excellent, if not the best starting point for all scientists who want to harness the power of network analysis for their field of expertise.

Towards an Information Theory of Complex Networks

Matthias Dehmer,Frank Emmert-Streib,Alexander Mehler
Towards an Information Theory of Complex Networks Book PDF

Author : Matthias Dehmer,Frank Emmert-Streib,Alexander Mehler
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 48,6 Mb
Release : 2011-08-26
Category : Mathematics
ISBN : 9780817649043

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Towards an Information Theory of Complex Networks by Matthias Dehmer,Frank Emmert-Streib,Alexander Mehler Pdf

For over a decade, complex networks have steadily grown as an important tool across a broad array of academic disciplines, with applications ranging from physics to social media. A tightly organized collection of carefully-selected papers on the subject, Towards an Information Theory of Complex Networks: Statistical Methods and Applications presents theoretical and practical results about information-theoretic and statistical models of complex networks in the natural sciences and humanities. The book's major goal is to advocate and promote a combination of graph-theoretic, information-theoretic, and statistical methods as a way to better understand and characterize real-world networks. This volume is the first to present a self-contained, comprehensive overview of information-theoretic models of complex networks with an emphasis on applications. As such, it marks a first step toward establishing advanced statistical information theory as a unified theoretical basis of complex networks for all scientific disciplines and can serve as a valuable resource for a diverse audience of advanced students and professional scientists. While it is primarily intended as a reference for research, the book could also be a useful supplemental graduate text in courses related to information science, graph theory, machine learning, and computational biology, among others.

Analysis of Complex Networks

Matthias Dehmer,Frank Emmert-Streib
Analysis of Complex Networks Book PDF

Author : Matthias Dehmer,Frank Emmert-Streib
Publisher : John Wiley & Sons
Page : 480 pages
File Size : 45,7 Mb
Release : 2009-07-10
Category : Medical
ISBN : 9783527627998

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Analysis of Complex Networks by Matthias Dehmer,Frank Emmert-Streib Pdf

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.

Network Science

Albert-László Barabási,Márton PÃ3sfai
Network Science Book PDF

Author : Albert-László Barabási,Márton PÃ3sfai
Publisher : Cambridge University Press
Page : 477 pages
File Size : 41,8 Mb
Release : 2016-07-21
Category : Computers
ISBN : 9781107076266

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Network Science by Albert-László Barabási,Márton PÃ3sfai Pdf

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