A variety of different social, natural and technological systems can be described by the same mathematical framework. This holds from the Internet to food webs and to boards of company directors. In all these situations a graph of the elements of the system and their interconnections displays a universal feature. There are only few elements with many connections, and many elements with few connections. This book presents the experimental evidence of these "Scale-free networks" and provides students and researchers with a corpus of theoretical results and algorithms to analyse and understand these features. The content of this book and the exposition makes it a clear textbook for beginners, and a reference book for the experts.

Many different systems both in nature and in technology can be described by means of networks of interconnected components. Despite their different aspects, all of them share similar mathematical properties. In this book we explain how to recognize these features and why these different systems develop this common structure.

Many different systems both in nature and in technology can be described by means of networks of interconnected components. Despite their different aspects, all of them share similar mathematical properties. In this book we explain how to recognize these features and why these different systems develop this common structure.

Expand your Python skills by working with data structures and algorithms in a refreshing context—through an eye-opening exploration of complexity science. Whether you’re an intermediate-level Python programmer or a student of computational modeling, you’ll delve into examples of complex systems through a series of exercises, case studies, and easy-to-understand explanations. You’ll work with graphs, algorithm analysis, scale-free networks, and cellular automata, using advanced features that make Python such a powerful language. Ideal as a text for courses on Python programming and algorithms, Think Complexity will also help self-learners gain valuable experience with topics and ideas they might not encounter otherwise. Work with NumPy arrays and SciPy methods, basic signal processing and Fast Fourier Transform, and hash tables Study abstract models of complex physical systems, including power laws, fractals and pink noise, and Turing machines Get starter code and solutions to help you re-implement and extend original experiments in complexity Explore the philosophy of science, including the nature of scientific laws, theory choice, realism and instrumentalism, and other topics Examine case studies of complex systems submitted by students and readers

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

Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems - Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience - Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain

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.