Citation impact is commonly assessed using direct, first-order citation relations. We consider here instead the indirect influence of publications on new publications via citations. We present a novel method to quantify the higher-order citation influence of publications, considering both direct, or first-order, and indirect, or higher-order citations. In particular, we are interested in higher-order citation influence at the level of disciplines. We apply this method to the whole Web of Science data at the level of disciplines. We find that a significant amount of influence -- 42% -- stems from higher-order citations. Furthermore, we show that higher-order citation influence is helpful to quantify and visualize citation flows among disciplines, and to assess their degree of interdisciplinarity.

中文翻译：

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量化科学出版物的高阶影响

引文影响通常使用直接的一阶引文关系进行评估。我们在这里考虑的是出版物通过引用对新出版物的间接影响。我们提出了一种新方法来量化出版物的高阶引用影响，同时考虑直接或一阶和间接或高阶引用。特别是，我们对学科层面的高阶引文影响感兴趣。我们将这种方法应用于学科层面的整个 Web of Science 数据。我们发现很大的影响——42%——源于高阶引用。此外，我们表明高阶引文影响有助于量化和可视化学科之间的引文流，并评估它们的跨学科程度。