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Diversity and network coherence as indicators of interdisciplinarity: case studies in bionanoscience

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The multidimensional character and inherent conflict with categorisation of interdisciplinarity makes its mapping and evaluation a challenging task. We propose a conceptual framework that aims to capture interdisciplinarity in the wider sense of knowledge integration, by exploring the concepts of diversity and coherence. Disciplinary diversity indicators are developed to describe the heterogeneity of a bibliometric set viewed from predefined categories, i.e. using a top-down approach that locates the set on the global map of science. Network coherence indicators are constructed to measure the intensity of similarity relations within a bibliometric set, i.e. using a bottom-up approach, which reveals the structural consistency of the publications network. We carry out case studies on individual articles in bionanoscience to illustrate how these two perspectives identify different aspects of interdisciplinarity: disciplinary diversity indicates the large-scale breadth of the knowledge base of a publication; network coherence reflects the novelty of its knowledge integration. We suggest that the combination of these two approaches may be useful for comparative studies of emergent scientific and technological fields, where new and controversial categorisations are accompanied by equally contested claims of novelty and interdisciplinarity.

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  1. In this study interdisciplinarity refers to all these types of cross-disciplinary research.

  2. Hereafter we will use only the term similarity, which is the one commonly used in bibliometrics.

  3. Simpson's diversity is defined as (1-Simpson Index), where the Simpson index is the commonly used measure of concentration (also known as Herfindahl-Hirschman Index in disciplines such as economics).

  4. Stirling index has become known in ecology literature as Rao's quadratic entropy (Rao 1982).

  5. One example could be ‘Nanoscience&Nanotechnology’ (N&N) from the ISI categorisation: according to Leydesdorff’s and Rafols’ metric (2009), N&N has a distance of only 0.0354 with ‘Materials Science, multidisciplinary’, whereas the distance between the latter and a relatively related field, such as ‘Physics, applied’, is 0.1916.

  6. Matrices of knowledge flows among disciplines are another way to present interdisciplinarity. E.g. Bourke and Butler (1998), calculated the number of publications from discipline-based departments associated to discipline-based journals. These matrices can then be used to compute similarity measures.

  7. Other publications use measures of diversity in bibliometrics, to examine not the diversity of disciplines, but diversity/concentration of research in institutions (e.g. Rousseau 2000).

  8. If the initial bibliometric set is large enough for statistical purposes, diversity can be computed directly from the SCs of the references.

  9. Simpson I and Stirling ∆, by definition, satisfy this condition. Variety N and Shannon H are normalised by dividing by their maximum values, N max and ln(N max), respectively, with N max being the total number of ISI SCs.

  10. Although co-citation analysis is the most extended technique to measure similarities between publications, it is impractical for our purposes for two reasons: first, it cannot be for used for recently published papers, due to lack of citations; second, it reflects similarities in the audience, rather than in the knowledge sources.

  11. Details of the scale invariance test are presented below.

    Network size






    Mean linkage strength






    Standard deviation per network






    Network realisations






    Standard deviation over realisations




    From a network of 1,275 publications on kinesin research, random subnetworks of different sizes were extracted. Mean linkage strength and standard deviation were computed for each. For small networks, multiple realisations were carried out to minimise statistical fluctuations.

  12. In one case, Noji 1997, we had to set the threshold at 0.025 in order to keep the network connected.

  13. More qualitative insights are described in Rafols and Meyer (2007) and Rafols (2007).

  14. This might explain, in part, the large difference between the SC distribution of ref-of-refs in Table 4 and the distribution of references among four selected disciplines reported in Rafols and Meyer (2007).

  15. The historical anecdote is that Paul D. Boyer, the author of this long review, was awarded the Nobel Prize precisely in 1997, thanks, in part, to the evidence provided by Noji and co-authors on his model of ATPase as a rotary motor.

  16. Two caveats apply to Fig. 8: (i) on average 30% of the references were published in Multidisciplinary Sciences journals; (ii) about 25% of the references are published in journals that are attributed to at least two SCs (which is why the publication SCs cannot be presented in one unique network).

  17. This is an inference from the qualitative interviews. Without quantitative benchmarks from other areas of science, the position of the case studies on the disciplinary diversity axis cannot be determined.

  18. The only processed input needed is the SC similarity matrix used to create the science map and compute Stirling ∆. This is available as a Pajek input file (Leydesdorff and Rafols 2009):


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This research was supported by an EU postdoctoral Marie-Curie Fellowship to IR, and the Daiwa Anglo-Japanese Foundation. We benefited from discussions with J. Gläser, L. Leydesdorff, F. Morillo, A.L. Porter, and SPRU colleagues S. Katz, R. Kempener, W.E. Steinmueller and A. Stirling.

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Correspondence to Ismael Rafols.

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Rafols, I., Meyer, M. Diversity and network coherence as indicators of interdisciplinarity: case studies in bionanoscience. Scientometrics 82, 263–287 (2010).

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