Complex Networks

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

This book aims to bring together researchers and practitioners working across domains and research disciplines to measure, model, and visualize complex networks. It collects the works presented at the

This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.

This book presents the features and advantages offered by complex networks in the machine learning domain. In the first part, an overview on complex networks and network-based machine learning is pres

"Network science is an emerging field of study that encompasses mathematics, computer science, physics, and engineering. An important issue in the study of complex networks is to understand the collec

In the last decade we have seen the emergence of a new inter-disciplinary field concentrating on the understanding large networks which are dynamic, large, open, and have a structure that borders orde

The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-expert

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.

In the last decade we have seen the emergence of a new inter-disciplinary field concentrating on the understanding large networks which are dynamic, large, open, and have a structure that borders orde

This book deals with the analysis of the structure of complex networks by combining results from graph theory, physics, and pattern recognition. The book is divided into two parts. 11 chapters are ded

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In th

Complex Social Networks is a newly emerging (hot) topic with applications in a variety of domains, such as communication networks, engineering networks, social networks, and biological networks. In th

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.

Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.

This text is a concise modern introduction to the science of complex networks, and is based on lectures for university students and non-specialists. The author aims to introduce a reader without seri

This text is a concise modern introduction to the science of complex networks, and is based on lectures for university students and non-specialists. The author aims to introduce a reader without seri

We live in a networked world. People are getting more and more interconnected through the new information and communication technologies, like mobile phones and the Internet.The function of cells can

The availability of large data sets has allowed researchers to uncover complex properties such as large-scale fluctuations and heterogeneities in many networks, leading to the breakdown of standard theoretical frameworks and models. Until recently these systems were considered as haphazard sets of points and connections. Recent advances have generated a vigorous research effort in understanding the effect of complex connectivity patterns on dynamical phenomena. This book presents a comprehensive account of these effects. A vast number of systems, from the brain to ecosystems, power grids and the internet, can be represented as large complex networks. This book will interest graduate students and researchers in many disciplines, from physics and statistical mechanics to mathematical biology and information science. Its modular approach allows readers to readily access the sections of most interest to them, and complicated maths is avoided so the text can be easily followed by non-expert

Power grids, flexible manufacturing, cellular communications: interconnectedness has consequences. This remarkable book gives the tools and philosophy you need to build network models detailed enough to capture essential dynamics but simple enough to expose the structure of effective control solutions. Core chapters assume only exposure to stochastic processes and linear algebra at undergraduate level; later chapters are for advanced graduate students and researchers/practitioners. This gradual development bridges classical theory with the state-of-the-art. The workload model at the heart of traditional analysis of the single queue becomes a foundation for workload relaxations used in the treatment of complex networks. Lyapunov functions and dynamic programming equations lead to the celebrated MaxWeight policy along with many generalizations. Other topics include methods for synthesizing hedging and safety stocks, stability theory for networks, and techniques for accelerated simulation

This book presents and explains the methods utilized to apply techniques from big data to massive structural data sets, especially those relating to the generation and analysis of very large networks

Community structure is a salient structural characteristic of many real-world networks. Communities are generally hierarchical, overlapping, multi-scale and coexist with other types of structural regu

This self-contained book presents theoretical results and current applications of structural network analysis to synthetic and real-world networks. The individual chapters are a careful balance of cl

Advances in complex networks and graph signal processing have important implications in fields ranging from communications and social networking to big data and biology. In Complex Networks, three pio

??This book combines game theory and complex networks to examine intentional technological risk through modeling. As information security risks are in constant evolution, the methodologies and t

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 technologic

This rigorous, self-contained book describes mathematical and, in particular, stochastic and graph theoretic methods to assess the performance of complex networks and systems. It comprises three parts: the first is a review of probability theory; Part II covers the classical theory of stochastic processes (Poisson, Markov and queueing theory), which are considered to be the basic building blocks for performance evaluation studies; Part III focuses on the rapidly expanding new field of network science. This part deals with the recently obtained insight that many very different large complex networks – such as the Internet, World Wide Web, metabolic and human brain networks, utility infrastructures, social networks – evolve and behave according to general common scaling laws. This understanding is useful when assessing the end-to-end quality of Internet services and when designing robust and secure networks. Containing problems and solved solutions, the book is ideal for graduate student

A modern introduction to synchronization phenomena, this text presents recent discoveries and the current state of research in the field, from low-dimensional systems to complex networks. The book describes some of the main mechanisms of collective behaviour in dynamical systems, including simple coupled systems, chaotic systems, and systems of infinite-dimension. After introducing the reader to the basic concepts of nonlinear dynamics, the book explores the main synchronized states of coupled systems and describes the influence of noise and the occurrence of synchronous motion in multistable and spatially-extended systems. Finally, the authors discuss the underlying principles of collective dynamics on complex networks, providing an understanding of how networked systems are able to function as a whole in order to process information, perform coordinated tasks, and respond collectively to external perturbations. The demonstrations, numerous illustrations and application examples will

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 s

In the modern world of gigantic datasets, which scientists and practioners of all fields of learning are confronted with, the availability of robust, scalable and easy-to-use methods for pattern recog

This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students and practitioners a unique update on the latest advances in theory, together with

This book provides a comprehensive review of complex networks from three different domains, presents novel methods for analyzing them, and highlights applications with accompanying case studies. Speci

This volume sheds light on the current state of complex networks and nonlinear dynamics applied to the understanding of economic and social phenomena ranging from geographical economics to macroeco

This book deals with the analysis of the structure of complex networks by combining results from graph theory, physics, and pattern recognition. The book is divided into two parts. 11 chapters are ded

Elucidating the spatial and temporal dynamics of how things connect has become one of the most important areas of research in the 21st century. Network science now pervades nearly every science domain

A state-of-the-art survey that reports on the progress made in selected areas of this important and growing field, aiding the analysis of existing networks and the design of new and more efficient alg