Entropy Maximization as a Holistic Design Principle for Complex Optimal Networks and the Emergence of Power Laws

Abstract

We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that the underlying organizing principle is to meet an overall performance target for wide-ranging operating or environmental conditions. This design or survival requirement of reliable performance under uncertainty leads, via the maximum entropy principle, to the emergence of a power law vertex degree distribution. The theory also predicts exponential or Poisson degree distributions depending on network redundancy, thus explaining all three regimes as different manifestations of a common underlying phenomenon within a unified theoretical framework.