# 7.1.5Quantification and measurement of interdisciplinarity

In order to make integrated knowledge measurable, one needs to determine the information sources associated with this knowledge. A proved bibliometric approach is the use of citation links, and in particular, the analysis of the reference lists of publications under study (e.g., Porter et al., 2007; Wang et al., 2015). As has been mentioned above, hybrid citation-lexical solutions may be used to improve scope and efficiency of this analysis. The quantification procedure is implemented through the determination and analysis of the frequencies of cited references. The findings by Zhang et al. (2016) obtained from a study of interdisciplinarity of journals suggest the reduction of measures to the use of an indicator pair, in particular, one indicator based on the distribution of cited references over disciplines in each individual document combining the two aspects of variety (number of items) and balance (distribution of items), and variety based on the similarity or dissimilarity of cited information sources for which a disciplinary distance matrix is required.  According to Zhang et al. (2016) we combine variety and balance in one indicator, particularly, the Inverse Simpson Index (2D):

$$^2D =\left( \displaystyle\sum_{i=1}^{N}{p_i^2}\right)^{-1}$$

where pi denotes the frequency of references. This index only depends on the distribution of cited references over disciplines, but does not use any information on their (dis-)similarity. This index can be supplemented by a measure of disparity for which we have chosen the Leinster-Cobbold disparity (2DS), that is,

​​​​​​​$$^2D^s =\left( \displaystyle \sum_{i,j=1}^{N}{(1-d_{ij})p_ip_j} \right)^{-1}$$

where dij denotes the dissimilarity of the disciplines i and j (cf. Glänzel et al., 2021). The application to distributions using different methods and granularity levels would, of course, result in different scales. In order to obtain commensurable scales, appropriate normalisation is required.

For this purpose, we proposed the method of Characteristic Scores and Scales (CSS). Similarly to the citation classes (cf. Glänzel et al., 2019), CSS can readily applied to practically any level of aggregation. Thus, for the two IDR measures 2D and 2DS, we define the four classes similar to the case of citations. Class 1 (CSS1) stands for low, Class 2 (CSS2) for fair, Class 3 (CSS3) for remarkable and Class 4 (CSS4) for outstanding standard of variety and disparity, respectively. Earlier studies (Glänzel and Debackere, 2021) have shown that the class distribution scores according to the two measures are practically uncorrelated, which means that both indexes indeed express complementary aspects of interdisciplinarity.