This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enume...

This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations. Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structur...

This book deals with averaging dynamics, a paradigmatic example of network based dynamics in multi-agent systems. The book presents all the fundamental results on linear averaging dynamics, proposing a unified and updated viewpoint of many models and convergence results scattered in the literature.Starting from the classical evolution of the powers of a fixed stochastic matrix, the text then considers more general evolutions of products of a sequence of stochastic matrices, either ...

This pioneering text provides a comprehensive introduction to systems structure, function, and modeling as applied in all fields of science and engineering. Systems understanding is increasingly recognized as a key to a more holistic education and greater problem solving skills, and is also reflected in the trend toward interdisciplinary approaches to research on complex phenomena. While the concepts and components of systems science will continue to be distributed throughout the various d...

This volume presents recent advances in the field of matrix analysis based on contributions at the MAT-TRIAD 2015 conference. Topics covered include interval linear algebra and computational complexity, Birkhoff polynomial basis, tensors, graphs, linear pencils, K-theory and statistic inference, showing the ubiquity of matrices in different mathematical areas.With a particular focus on matrix and operator theory, statistical models and computation, the International Conference on M...

This book follows the methodologies of complex adaptive systems research in their application to addressing the problems of terrorism, specifically terrorist networks, their structure and various methods of mapping and interdicting them as well as exploring the complex landscape of network-centric and irregular warfare. A variety of new models and approaches are presented here, including Dynamic Network Analysis, DIME/PMESII models, percolation models and emergent models of insurgency. In ...

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance.The book is self-contained, and requires only an undergraduate mathematical background.

Dynamical models on graphs or random graphs are increasingly used in applied sciences as mathematical tools to study complex systems whose exact structure is too complicated to be known in detail. Besides its importance in applied sciences, the field is increasingly attracting the interest of mathematicians and theoretical physicists also because of the fundamental phenomena (synchronization, phase transitions etc.) that can be studied in the relatively simple framework of dynamical models...

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties.Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discu...

With the unifying theme of abstract evolutionary equations, both linear and nonlinear, in a complex environment, the book presents a multidisciplinary blend of topics, spanning the fields of theoretical and applied functional analysis, partial differential equations, probability theory and numerical analysis applied to various models coming from theoretical physics, biology, engineering and complexity theory.Truly unique features of the book are: the first simultaneous presentation...

This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it discusses in detail the significance of this nucleation effect for traffic and transportation th...

This book collects the works presented at the 8th International Conference on Complex Networks (CompleNet) 2017 in Dubrovnik, Croatia, on March 21-24, 2017. CompleNet aims at bringing together researchers and practitioners working in areas related to complex networks. The past two decades has witnessed an exponential increase in the number of publications within this field. From biological systems to computer science, from economic to social systems, complex networks are becoming pervasive...