Scale Free Networks

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.

Dive into Python's advanced possibilities, including algorithm analysis, graphs, scale-free networks, and cellular automata with this in-depth, hands-on guide.

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

A heuristic argument was presented in favor of hypothesis that scientific communication corresponds to a process known as scale-free network.

We live in a world of networks, where everything is amazingly close to everything else. The notion of 'network' turns out to be central to our times: the Internet and WWW are changing our lives; our physical existence is based on various biological networks; we are involved in all-enveloping networks of economic and social relations. Only in the 1990s did physicists begin to explore real networks, both natural and artificial, as evolving systems with intriguingly complex and effective architectures. Progress has been so immediate and astounding that we actually face a new science based on a new set of concepts, and, one may even say, on a new philosophy: the natural philosophy of a small world. Old ideas from mathematics, statistical physics, biology, computer science, and so on take on quite new forms in applications to real evolving networks. - What is common to all networks? - What are the general principles of the organization and evolution of networks? - How do the laws of nature work in communication, biological, and social networks? - What are networks? This book, written by physicists, answers these questions and presents a general insight into the world of networks.

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.

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

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 and a multitude of applications. It presents the peer-reviewed proceedings of the VI International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2017), which took place in Lyon on November 29 – December 1, 2017. The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and ecological networks and technological networks.