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I would like to thank the authors for the significant efforts they have made to revise their paper. Like in my previous review, my comments will focus on Section 2, in which the authors present their framework for characterizing interdisciplinary knowledge flow (IKF). Despite the efforts made by the authors, I’m afraid there are still important problems in this section.
In their revised paper, the authors have added a more extensive conceptual discussion. They have also added an appendix in which they analyze the mathematical properties of their proposed indicators. Despite these improvements, I still find it difficult to make sense of the framework introduced in Section 2. One problem is that the authors first introduce their indicators and then provide a conceptual discussion. This should be the other way around. The authors should first discuss at a conceptual level how they understand the idea of IKF and what they consider to be the key aspects of IKF that they want to quantify using bibliometric indicators. They should then present the indicators and show how each of the indicators captures one of the aspects of IKF introduced in the conceptual discussion. Mathematical results should be included in the paper only if they have a clear added value. Mathematical details can be presented in an appendix, but the key insights resulting from a mathematical analysis should be integrated in the discussion of the framework in Section 2.
In my view, the authors still haven’t managed to convincingly motivate and explain the framework they introduce in Section 2. I believe the definition of intensity would be more intuitively reasonable if M_{ij} \delta_{i} in the denominator is simplified to \delta_{i}. This would make intensity easier to understand and it would strengthen the connection between intensity and broadness. Since the denominator of intensity would be identical to the numerator of broadness, the product of intensity and broadness would have a natural interpretation, namely the average number of citations to papers in entity Y in papers in entity X. This can be seen as an overall indicator of IKF, and intensity and broadness then provide an elegant decomposition of this overall indicator.
It remains unclear to me how heterogeneity fits in the framework proposed by the authors. There is no clear connection between heterogeneity on the one hand and intensity and broadness on the other hand. Also, as the authors explain, heterogeneity is about differences between two entities in their knowledge base. The relation with IKF is not clear to me. The size-dependence of heterogeneity also feels counterintuitive to me. The authors state that “the objective of heterogeneity is not to directly quantify the IKF between disciplines but to transform prior knowledge regarding the cognitive distance between disciplines into concrete measurements. It can be utilized as a ‘base map’ when validating findings or deciphering universal patterns of IKF.” I find this hard to understand. If heterogeneity does not ‘directly quantify IKF’, then how can it be used to ‘validate findings’? And what does it mean to ‘decipher universal patterns of IKF’? My impression is that the authors do not have a clear idea themselves about the role of heterogeneity in their proposed framework.