Citation cascade and the evolution of topic relevance

Citation analysis, as a tool for quantitative studies of science, has long emphasized direct citation relations, leaving indirect or high‐order citations overlooked. However, a series of early and recent studies demonstrate the existence of indirect and continuous citation impact across generations. Adding to the literature on high‐order citations, we introduce the concept of a citation cascade: the constitution of a series of subsequent citing events initiated by a certain publication. We investigate this citation structure by analyzing more than 450,000 articles and over 6 million citation relations. We show that citation impact exists not only within the three generations documented in prior research but also in much further generations. Still, our experimental results indicate that two to four generations are generally adequate to trace a work's scientific impact. We also explore specific structural properties—such as depth, width, structural virality, and size—which account for differences among individual citation cascades. Finally, we find evidence that it is more important for a scientific work to inspire trans‐domain (or indirectly related domain) works than to receive only intradomain recognition in order to achieve high impact. Our methods and findings can serve as a new tool for scientific evaluation and the modeling of scientific history.