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Betweenness and Diversity in Journal Citation Networks as Measures of Interdisciplinarity -- A Tribute to Eugene Garfield --

Loet Leydesdorff, Caroline S. Wagner, Lutz Bornmann

arXiv:1705.03272v2cs.DL

TL;DR

Interdisciplinarity is difficult to operationalize when disciplines cannot be clearly demarcated and the term remains fluid. Diversity can be decomposed into cell-value contributions through straightforward summation. Betweenness centrality is better viewed as a measure of multidisciplinarity, while diversity in the cited dimension may come closest to interdisciplinarity.

  • Problem

    Interdisciplinarity is difficult to operationalize when disciplines cannot be clearly demarcated and the term remains fluid.

    Source: Conclusions and discussion · p. 38

  • Method

    Diversity can be decomposed into cell-value contributions through straightforward summation.

    Source: §2 · p. 5, §1.2.2 · p. 13

  • Results

    Betweenness centrality is better viewed as a measure of multidisciplinarity, while diversity in the cited dimension may come closest to interdisciplinarity.

    Source: Conclusions and discussion · p. 39

  • Takeaways & Limitations

    Diversity in the cited direction is a candidate journal-level indicator of interdisciplinarity, not a definitive measure.

    Source: Conclusions and discussion · p. 39

    Knowledge integration and diffusion refer to diversity but not necessarily to interdisciplinarity.

    Source: Conclusions and discussion · p. 40

Abstract

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Journals were central to Eugene Garfield's research interests. Among other things, journals are considered as units of analysis for bibliographic databases such as the Web of Science (WoS) and Scopus. In addition to disciplinary classifications of journals, journal citation patterns span networks across boundaries to variable extents. Using betweenness centrality (BC) and diversity, we elaborate on the question of how to distinguish and rank journals in terms of interdisciplinarity. Interdisciplinarity, however, is difficult to operationalize in the absence of an operational definition of disciplines, the diversity of a unit of analysis is sample-dependent. BC can be considered as a measure of multi-disciplinarity. Diversity of co-citation in a citing document has been considered as an indicator of knowledge integration, but an author can also generate trans-disciplinary--that is, non-disciplined--variation by citing sources from other disciplines. Diversity in the bibliographic coupling among citing documents can analogously be considered as diffusion of knowledge across disciplines. Because the citation networks in the cited direction reflect both structure and variation, diversity in this direction is perhaps the best available measure of interdisciplinarity at the journal level. Furthermore, diversity is based on a summation and can therefore be decomposed, differences among (sub)sets can be tested for statistical significance. In an appendix, a general-purpose routine for measuring diversity in networks is provided.

1. Introduction

The paper asks how journals can be distinguished and ranked by interdisciplinarity when disciplinary boundaries are difficult to define. It examines citation-based measures while separating network decomposition from the semantic interpretation of interdisciplinarity.

1. Introduction

  • Conventional subject categories rely on heuristic assignments that can obscure cross-boundary relatedness and disadvantage developments combining disparate ideas.Source: §1 · pp. 2–3
  • The study adopts definitions in which multidisciplinarity juxtaposes separate perspectives, interdisciplinarity integrates disciplines, and transdisciplinarity synthesizes them into larger frameworks.Source: §1 · p. 3
  • The study revisits how to distinguish and rank journals by interdisciplinarity to identify where creative combinations of information are indicated.Source: §1 · p. 3
  • The analysis builds on a statistical decomposition of 11,365 JCR 2015 journals using VOSviewer.Source: §1 · p. 3
  • Because statistical decomposition need not be semantically meaningful, the approach separates decomposition from the question of interdisciplinarity.Source: §1 · pp. 3–4

2. Betweenness centrality—the relative number of times that a node is part of the shortest

This section examines how betweenness centrality and diversity can be used to measure journal interdisciplinarity in citation networks, where disciplinary boundaries and the unit and sample of analysis shape the measurement. It also considers diversity decomposition as a means of comparing groups statistically.

2. Betweenness centrality—the relative number of times that a node is part of the shortest

  • Diversity can be decomposed into cell-value contributions, and differences among aggregated contributions can be tested with ANOVA and post-hoc Bonferroni correction.The cited method gives Tukey tests as an example of post-hoc testing.Source: §2 · p. 5

1.1. “Interdiscipinarity”

  • Because disciplines and journal boundaries are difficult to define, the study asks how to measure journal interdisciplinarity at different levels and what measurement problems arise.Source: §1.1 · pp. 7–9

1.2 The measurement instruments

  • The study focuses on betweenness centrality and diversity as its two measures of interdisciplinarity.Source: §1.2 · p. 9

1.2.1. Betweenness centrality

  • Betweenness centrality and derivatives such as structural holes are readily available in software packages.Source: §1.2.1 · p. 9
  • Betweenness centrality indicates how often a node lies on shortest paths between other nodes, positioning it to broker or control information flow between clusters.The further extension combining betweenness with disparity is not studied here.Source: §1.2.1 · pp. 9–10

1.2.2. Diversity

  • The diversity formulation combines variety and disparity but does not include balance, another aspect distinguished in accounts of interdisciplinarity.Variety reflects the distribution across categories, while disparity reflects distances among them.Source: §1.2.2 · pp. 10, 11, 13
  • Diversity in citing patterns has been treated as knowledge integration, whereas diversity in cited structures represents diffusion that can be interdisciplinary to varying extents.The cited structures act as selection environments.Source: §1.2.2 · p. 12
  • Because diversity is a summation, it can be decomposed by cell values p_i p_j d_ij, and aggregated subsets can be compared using ANOVA with Bonferroni-corrected post-hoc tests.The proposed decomposition uses the WoS Category Library and Information Science set of 86 journals in JCR 2015.Source: §1.2.2 · p. 13

1.3. Units of analysis

  • Interdisciplinarity depends on the unit and sample: socially organized groups and intellectually organized fields are distinct levels, and journal assessments vary with the sample.Source: §1.3 · pp. 13–15
  • A journal may appear interdisciplinary in a large set of journals but lose that appearance when the set is decomposed.The result depends on the analysis granularity and how disciplinary borders are drawn.Source: §1.3 · p. 15
  • Decomposition can cut important ties to other domains, affecting judgments of interdisciplinarity.Source: §1.3 · p. 15
  • Measuring interdisciplinarity unavoidably entails a model, through which the concept is reconstructed.Source: §1.3 · p. 15

2. Methods

The methods analyze a directed journal-citation matrix from JCR 2015, decomposing it into journal groups and evaluating betweenness centrality and Rao–Stirling diversity. Diversity is measured in either citation direction, with cosine-based distance used for the analysis.

2.1. Data

  • 11,359 journals form the largest connected component of the directed, valued JCR 2015 matrix; six of the 11,365 listed journals are unconnected.Source: §2.1 · p. 15
  • Ten clusters are distinguished in the first decomposition; analyses cover all 11,359 connected journals, the 3,274-journal first cluster, and its 62 LIS journals.Source: §2.1 · p. 16

2.2. Statistics

  • Betweenness centrality for a journal is the proportion of geodesics between vertex pairs that include it.Source: §2.2 · pp. 16–17
  • Rao–Stirling diversity and 2D3 are evaluated on vectors in either the cited or citing direction, using proportions and distances from that same direction.Source: §2.2 · p. 17
  • The average geodesic is 2.5 with a standard deviation of 0.6, so the analysis uses 1 – cosine as its distance measure.Source: §2.2 · p. 18

3. Results

The results examine how betweenness centrality (BC) and diversity capture citation patterns across the full journal set, the social-science subset, and LIS journals. The LIS analysis reports rankings for 86 journals classified as LIS in JCR 2015 and describes how diversity patterns vary across levels of aggregation.

3.1. The full set of 11,365 journals in JCR 2015

  • Scientometrics ranks 11th on binary BC but 15th on valued BC, reflecting incidental cross-field citations alongside denser citation within its own intellectual environment.The authors characterize it as a specialist journal whose citation patterns nevertheless span disciplines.Source: §3.1 · pp. 19, 21
  • The reported ranking correlation across the file is larger than .99; PLOS ONE and Psychol Bull gain score when BC is based on values, whereas Nature and Science lose.Source: §3.1 · p. 19
  • For the full set, citing-direction diversity is uncorrelated with BC, whereas cited-direction diversity retains a substantial rank-order correlation with BC.The authors distinguish diversity’s variety component from BC’s bridging of disciplinary distances.Source: §3.1 · p. 21
  • The Journal of the Chinese Institute of Engineering has 2D3 = 20.13 at the top of the diversity list; it was cited in 56 journals and cites from 230, making it a net importer of knowledge.Its citing-diversity map prominence contrasts with its lack of visibility in the BC map.Source: §3.1 · p. 22, Figure 2 · p. 23

3.2. Journals in the Social Sciences

  • In the social-science subset, Soc Sci Med ranks highest on BC in both analyses, while Scientometrics falls from 11th to 21st in binary BC and 15th to 31st in valued BC.The decomposition removes its betweenness connecting social sciences with natural and medical sciences.Source: §3.2 · p. 24
  • Two factors explain 78.6% of variance in the four social-science measures, and citing-direction diversity correlates with binary and valued BC at .010 and .008, respectively.The analysis describes the mechanisms as orthogonal.Source: §3.2 · p. 26, Table 7 · p. 26
  • In social sciences, citing-direction diversity highlights highly diverse journals spread across disciplines, while the BC map shifts attention toward applied journals.The examples include Appl Econ and World Dev, which come to the foreground in the BC map.Source: §3.2 · pp. 27, 29

3.3. Library and information sciences (LIS)

  • For its LIS results, the analysis uses citations among 86 journals classified as LIS in JCR 2015 and presents top-25 rankings across BC and diversity measures.The paper notes that it first analyzed 62 journals classified as LIS, but reports the 86-journal results here for presentation.Source: §3.3 · p. 29, Table 8 · p. 30
  • Scientometrics had the highest BC in both analyses but ranked 45th in citing diversity and 70th in cited diversity; JASIST ranked 12th in BC and third in citing diversity.Source: §3.3 · p. 31
  • In the smaller LIS set, citing diversity was significantly correlated with BC, suggesting that specialty-level citing behavior is more specific and guided by the field’s socio-cognitive structure.Source: §3.3 · p. 31
  • For Scientometrics, citing diversity exceeded cited diversity in the full set, but cited diversity was larger in the social-sciences subset; within LIS, the journal cited more than it was cited.Source: §3.3 · p. 31, Table 10 · p. 32
  • Diversity depends on how the sample in which it is measured is delineated.Source: §3.3 · p. 32

4. Decomposition of the diversity

The LIS diversity analysis decomposes journals into subgroups and tests within- and between-group diversity. The results show that subgrouping concentrates diversity in a minority of citation-pair cells, while between-group diversity differs significantly from most subgroup values.

4. Decomposition of the diversity

  • The LIS set was decomposed into six groups, including one single-journal group; three journals outside the large component were excluded.Figures 4 and 5 show the clustering and average cited and citing diversity for five subgroups.Source: §4 · p. 32, Figure 4 · p. 33, Figure 5 · p. 34
  • In the citing dimension, library science and bibliometrics formed a high-diversity homogeneous group, distinct from the other three groups’ significantly lower scores.The distinction was not present in the cited dimension.Source: §4 · p. 34
  • Between-group diversity is defined as total diversity minus the sum of within-group diversities, with subset scores calculated from corresponding submatrices.The analysis also reports diversity values after normalizing cell values to the grand matrix.Source: §4 · p. 35
  • Between-group diversity differed significantly from all subgroup values except citing diversity in the information-science subset; cited diversity in the set was statistically homogeneous.Information science and library science were considered homogeneous with between-group diversity; the other three specialisms were not.Source: §4 · pp. 34–35
  • Within-group diversity accounted for 53.3% of cited and 58.1% of citing total diversity, although within-group subsets comprised only 24.8% of the cells.The remaining between-group shares were 46.7% and 41.9%, respectively.Source: §4 · p. 36

5. Diffusion and Integration

The paper distinguishes knowledge integration from diffusion through citation-network relations and illustrates both networks for Scientometrics in the LIS journal set. The examples are restricted to that set of 86 journals.

5. Diffusion and Integration

  • Co-citation links sources cited together by a citing unit, while bibliographic coupling links citing units that share cited sources.The paper treats the former as integration and the latter as diffusion of knowledge, respectively.Source: §5 · p. 36
  • The integration and diffusion networks are drawn from cited- and citing-diversity relations by extracting k=1 neighbourhoods.Figures 6A and 6B provide the networks for Scientometrics in the LIS set.Source: §5 · p. 36
  • For Scientometrics, 38 journals constitute the diffusion network and 51 the knowledge-integration network.The two network counts are based on the LIS set of 86 journals.Source: §5 · pp. 36, 38
  • JASIST is central in the integration network, whereas its current-name journal appears in the diffusion network; the analysis excludes journals outside LIS.The paper identifies the current name as the Journal of the Association for Information Science and Technology.Source: §5 · p. 38

Conclusions and discussion

The discussion distinguishes multi-disciplinarity from interdisciplinarity and treats diversity in the cited direction as the closest available indicator of interdisciplinarity. Yet disciplines remain difficult to operationalize, and diversity scores depend on the system of reference.

Conclusions and discussion

  • Betweenness centrality (BC) indicates multi-disciplinarity more than interdisciplinarity, and valued BC improves on binary BC because citation links are not equal.The discussion therefore cautions against treating marginal links as equivalent to stronger links.Source: Conclusions and discussion · p. 39
  • Citing-direction diversity is statistically independent of BC and may reflect non- or trans-disciplinary variation, while specialist contexts can couple it to the intellectual structures studied.The interpretation therefore depends on whether the context is local or applicational, or specialist.Source: Conclusions and discussion · p. 39
  • Cited-direction diversity may come closest to interdisciplinarity, understood as a trade-off between structural selection and stochastic variation.The authors propose variation and selection as a potentially more fruitful conceptualization.Source: Conclusions and discussion · pp. 39, 41
  • Rao–Stirling diversity is often used as an interdisciplinarity indicator despite omitting balance, but it remains an indicator of diversity.Knowledge integration and diffusion refer to diversity, not necessarily interdisciplinarity.Source: Conclusions and discussion · pp. 39–40
  • The diversity sum can be decomposed into within- and between-group components, and differences can be tested for significance to distinguish homogeneous from non-homogeneous subsets.The discussion specifies Bonferroni correction for these post hoc tests.Source: Conclusions and discussion · p. 40
  • The paper provides an appendix routine for generating diversity scores from networks, while leaving the interpretation of diversity as interdisciplinarity unresolved.The authors demonstrate integration and diffusion networks using an example.Source: Conclusions and discussion · pp. 39–40
  • Multi-disciplinarity is operationalizable, but interdisciplinarity remains difficult to define without operational disciplinary boundaries.The paper notes that the operationalization problem remains unsolved in bibliometrics.Source: Conclusions and discussion · pp. 38, 40
  • Diversity scores depend on the system of reference, so analysts should specify relevant contexts, such as journal sets or comparable departments, before evaluating networks.The authors recommend valued BC when networks are measured at the interval scale.Source: Conclusions and discussion · pp. 40–41
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