## Complex Webs: Anticipating the ImprobableComplex 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. |

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asymptotic attractor autocorrelation function average B.J. West behavior calculated chaos clustering coefﬁcient complex webs Consequently constant curve deﬁned deﬁnition derivative described determined deterministic diffusion discussed distribution density entropy equations of motion equilibrium exponent exponential ﬁeld Figure ﬁnd ﬁnite ﬁrst ﬁt ﬂow ﬂuctuations fractal dimension fractional calculus frequency Gaussian given graph Hamiltonian Hurst exponent hyperbolic hyperbolic distribution inﬁnite inﬂuence integral interactions interval inverse power inverse power-law Langevin equation Laplace transform linear long-time master equation mathematical measure neurons nonlinear normal normal statistics obtain oscillator parameter particle perturbation phase space phenomena Phys physical Poisson Poisson distribution power-law index prediction probability density properties random force random walk relation Reproduced with permission response result scale-free scaling sciences scientiﬁc solution speciﬁc statistics stochastic theory trajectory variance velocity waiting-time distribution yields Zipf’s law