Temporal rich club phenomenon and its formation mechanisms

The temporal rich club (TRC) phenomenon is widespread in real systems, forming a tight and continuous collection of the prominent nodes that control the system. However, there is still a lack of sufficient understanding of the mechanisms of TRC formation. Here we use the international N-nutrient trade network as an example of an in-depth identification, analysis, and modeling of its TRC phenomenon. The system exhibits a statistically significant TRC phenomenon, with eight economies forming the cornerstone club. Our analysis reveals that node degree is the most influential factor in TRC formation compared to other variables. The mathematical evolution models we constructed propose that the TRC in the N-nutrient trade network arises from the coexistence of degree-homophily and path-dependence mechanisms. By comprehending these mechanisms, we introduce a different perspective on TRC formation. Although our analysis is limited to the international trade system, the methodology can be extended to analyze the mechanisms underlying TRC emergence in other systems.