From Parts-to-Whole: A Holistic Theory of Optimal Design and Adaptation in Complex Networks

Recent research in network science has shown that complex networks in diverse application areas seem to exhibit several universal features. In this paper, we describe a holistic theory of optimal design and adaptation of complex networks based on the universal organizing principle of network structure optimization to meet overall survival or performance objectives. We demonstrate how a network self-organizes by evolutionary adaptation to maximize its survival or performance fitness, which in turns depends, under given environmental survival pressure, on the network’s efficiency, robustness and cost. The theory provides a general conceptual framework for integrating network topology with survival objectives, selection pressures, evolutionary adaptation and performance optimization in a single coherent formalism. Further, we investigate another related and important question, namely, how “parts-level ” network properties such as the vertex degree determine “system-level ” properties such as survival or performance. We also examine the implications of uncertainty in the environment on optimal network design. Using the concepts of interaction ‘values ’ and network ‘satisfaction ’ as generic performance measures, we show that the underlying organizing principle is to meet an overall performance target with reliable performance under maximum environmental uncertainty. This leads to the emergence of the power law degree distribution, often displayed in complex networks, as a consequence of the Maximum Entropy Principle. This notion also leads to other distributions under various limiting conditions