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.

中文翻译：

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引文级联与主题相关性的演变

引文分析作为科学定量研究的一种工具，长期以来一直强调直接引文关系，而忽略了间接或高阶引文。然而，一系列早期和最近的研究证明了跨代间接和连续引用影响的存在。除了关于高阶引用的文献之外，我们还引入了引用级联的概念：由某个出版物引发的一系列后续引用事件的构成。我们通过分析超过 450,000 篇文章和超过 600 万条引文关系来研究这种引文结构。我们表明，引文影响不仅存在于先前研究中记录的三代人中，而且还存在于更远的代人中。仍然，我们的实验结果表明，两到四代通常足以追踪作品的科学影响。我们还探索了特定的结构特性——例如深度、宽度、结构病毒式传播和大小——这些特性解释了各个引文级联之间的差异。最后，我们发现有证据表明，对于一项科学工作来说，激发跨领域（或间接相关领域）的工作比仅获得领域内的认可更重要，以实现高影响力。我们的方法和发现可以作为科学评估和科学历史建模的新工具。我们发现有证据表明，对于一项科学工作来说，激发跨领域（或间接相关领域）的工作比仅获得领域内的认可更重要，以实现高影响力。我们的方法和发现可以作为科学评估和科学历史建模的新工具。我们发现有证据表明，对于一项科学工作来说，激发跨领域（或间接相关领域）的工作比仅获得领域内的认可更重要，以实现高影响力。我们的方法和发现可以作为科学评估和科学历史建模的新工具。