Understanding complex systems: Using interaction as a measure of emergence

Understanding the behavior of complex systems is becoming a crucial issue as systems grow in size, and the interconnection and geographical distribution of their components diversifies. The interaction over time of many components often leads to emergent behavior, which can be harmful to the system. Despite this, very few practical approaches for the identification of emergent behavior exist, and many are unfeasible to implement. Approaches using interaction as a measure of emergence have the potential to alleviate this problem. In this paper, we analyse absolute and relative methods that use interaction as a measure of emergence. Absolute methods compute a degree of interaction that characterizes a system state as being emergent. Relative methods compare interaction graphs of the system state with interaction graphs of systems that have been shown previously to exhibit emergence. We present these approaches and discuss their advantages and limitations using theoretical and experimental analysis.