Complex Webs: Anticipating the Improbable

Abstract

"Complex Webs synthesises modern mathematical developments with a broad range of complex network applications of interest to the engineer and system scientist, presenting the common principles, algorithms, and tools governing network behaviour, dynamics, and complexity. The authors investigate multiple mathematical approaches to inverse power laws and expose the myth of normal statistics to describe natural and man-made networks. Richly illustrated throughout with real-world examples including cell phone use, accessing the Internet, failure of power grids, measures of health and disease, distribution of wealth, and many other familiar phenomena from physiology, bioengineering, biophysics, and informational and social networks, this book makes thought-provoking reading. With explanations of phenomena, diagrams, end-of-chapter problems, and worked examples, it is ideal for advanced undergraduate and graduate students in engineering and the life, social, and physical sciences. It is also a perfect introduction for researchers who are interested in this exciting new way of viewing dynamic networks"-- "The Italian engineer turned social scientist Vilfredo Pareto was the first investigator to determine that the income in western society followed a law that was fundamentally unfair. He was not making a value judgement about the poor and uneducated or about the rich and pampered; rather, he was interpreting the empirical finding that in 1894 the distribution of income in western societies was not "normal," but instead the number of people with a given income decreased as a power of the level of income. On bi-logarithmic graph paper this income distribution graphs as a straight-line segment of negative slope and is called an inverse power law. He interpreted his findings as meaning that a stable society has an intrinsic imbalance resulting from its complex nature, with the wealthy having a disproportionate fraction of the available wealth. Since then staggeringly many phenomena from biology, botany, economics, medicine, physics, physiology, psychology, in short every traditional discipline, have been found to involve complex phenomena that manifest inverse power-law behavior"--