Network entropy as a key to the past: A quantitative approach to complex social networks

The quantification of adaptive cycles in complex systems remains a significant challenge, particularly in archaeological contexts where traditional approaches rely heavily on qualitative assessments. This paper presents PANARCH (Phase Analysis of Network Adaptive Research & Complex Hierarchies), a methodological framework that integrates four complementary entropy measures—degree, eigenvector, community, and betweenness entropy—to identify and quantify adaptive cycle phases in complex networks. The framework enables systematic detection of phase transitions and provides mathematical signatures for different system states, advancing beyond single-metric analyses. We validate this approach through a detailed case study of archaeological networks from Eastern Iberia (5300-3800 cal BP), analyzing lithic arrowhead similarity patterns across multiple temporal windows. The results reveal structured patterns of social transformation, with entropy variations successfully identifying different phases of the adaptive cycle. PANARCH demonstrates particular utility in archaeological contexts where preservation biases often complicate traditional analyses, while offering broader applications for studying complex system dynamics across disciplines where phase transitions and system reorganization are key concerns.