Hypernetworks in the Science of Complex Systems

The modern world is complex beyond human understanding and control. The science of complex systems aims to find new ways of thinking about the many interconnected networks of interaction that defy traditional approaches. Thus far, research into networks has largely been restricted to pairwise relationships represented by links between two nodes. This volume marks a major extension of networks to multidimensional hypernetworks for modeling multi-element relationships, such as companies making up the stock market, the neighborhoods forming a city, people making up committees, divisions making up companies, computers making up the internet, men and machines making up armies, or robots working as teams.

This volume makes an important contribution to the science of complex systems by: (i) extending network theory to include dynamic relationships between many elements; (ii) providing a mathematical theory able to integrate multilevel dynamics in a coherent way; (iii) providing a new methodological approach to analyze complex systems; and (iv) illustrating the theory with practical examples in the design, management and control of complex systems taken from many areas of application.

Contents:

• Introduction
• Sets and Relations
• Hypergraphs and the Galois Lattice
• Simplicial Complexes and Q-Analysis
• Backcloth and Traffic: Dynamics Constrained by Topology
• Hypernetworks
• Multilevel Systems
• Time, Events, Prediction and Forecasting
• Hypernetworks and Design
• Policy, Design, Planning and Science
• Notes and Reflections

Readership: Academics: researchers, scientists, social scientists, complex systems scientists, economists, biologists; Industry: managers, planners, consultants, knowledge professionals, systems engineers, automation specialists, supply chain managers; Public services: Council Officers, city planners, transport planners, health professionals, welfare professionals.
Key Features:

• A first book of its kind on 'hypernetworks', a term the author has coined to describe the mathematical structures he has worked on over the last 30 years
• Introduces hypernetworks in the context of examples drawn from a wide range of fields, including design, planning, management, art, neural network, machine vision, robotics, traffic, road accidents, amongst others
• The emphasis of this volume is on useful and added-value applications. It will develop the necessary mathematics and assuming no pre-requisites
• Contains a myriad of illustrations to further understand the topics discussed