Entropy maximization as a holistic design principle for complex optimal networks

Abstract

AbstractA general holistic theory is presented for the organization of complex networks. The theory proposes that complex networks, both human‐engineered and naturally evolved, are organized to meet certain design or survival objective(s) for a wide variety of operating or environmental conditions. Using the concepts of “value ” of interactions and “satisfaction ” in a network as generic performance measures, we show that the underlying organizing principle is to meet an overall performance target for a wide variety of operating environments as the design objective. This design requirement for reliable performance under maximum uncertainty leads to the emergence of power laws as a consequence of the Maximum Entropy Principle. The theory also predicts the emergence of exponential and Poisson distribution regimes as a function of the redundancy of the network, thus explaining all three regimes as different manifestations of the same underlying phenomenon within a unified theoretical framework. © 2005 American Institute of Chemical Engineers AIChE J, 2006