Entropy maximization as a holistic design principle for complex optimal networks

Abstract

A 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.