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"Betweenness Centrality" as an Indicator of the "Interdisciplinarity" of Scientific Journals
Loet Leydesdorff
TL;DR
The paper addresses the difficulty of identifying interdisciplinarity when journal classifications are fuzzy and journals span multiple intellectual traditions. It analyzes centrality measures across 7,379 journals and local citation environments using normalized citation-pattern vector spaces. It finds that betweenness centrality indicates journal interdisciplinarity in local environments after normalization, while size otherwise obscures the measure.
Problem
Journal interdisciplinarity is difficult to assess because classifications are fuzzy and journals may span multiple intellectual traditions.
Method
The paper analyzes degree, betweenness, and closeness centrality across 7,379 journals and local citation environments using citation-pattern vector spaces.
Results
Betweenness centrality is shown to indicate journal interdisciplinarity in local citation environments after normalization.
Takeaways & Limitations
Betweenness centrality is useful as an interdisciplinarity indicator when applied locally and with normalization.
Takeaways & Limitations
Unambiguous classification of journal sets from aggregated citation patterns is impossible because the space is multidimensional and its subsets are fuzzy.
Abstract
from arXiv · showhide
In addition to science citation indicators of journals like impact and immediacy, social network analysis provides a set of centrality measures like degree, betweenness, and closeness centrality. These measures are first analyzed for the entire set of 7,379 journals included in the Journal Citation Reports of the Science Citation Index and the Social Sciences Citation Index 2004, and then also in relation to local citation environments which can be considered as proxies of specialties and disciplines. Betweenness centrality is shown to be an indicator of the interdisciplinarity of journals, but only in local citation environments and after normalization because otherwise the influence of degree centrality (size) overshadows the betweenness-centrality measure. The indicator is applied to a variety of citation environments, including policy-relevant ones like biotechnology and nanotechnology.
1. Introduction
Journal-based interdisciplinarity is difficult to assess because disciplinary sets are fuzzy, journals can span multiple disciplines, and cross-disciplinary developments blur established classifications. The paper therefore seeks an individual-journal indicator before delineating interdisciplinary journal groups.
- Indicator limitations: Discipline-specific journal sets remain difficult to operationalize because their boundaries and definitions are disputed.The paper contrasts researcher-based groupings with groupings derived from aggregated journal citation patterns.
- Indicator limitations: Existing journal indicators include impact factors, immediacy indices, and subject categories, but subject categorization is considered the least objective because it is not citation-based.ISI staff assign journals to subjects using criteria including titles and citation patterns.
- Interdisciplinary boundaries: Journals may belong to more than one discipline, making comparisons within a single disciplinary reference group problematic.The paper identifies journal interdisciplinarity as a source of difficulty for journal-level comparison.
- Interdisciplinary boundaries: Interdisciplinary developments can arise at interfaces among established fields, as illustrated by nanotechnology across applied physics, chemistry, and materials science.The paper contrasts nanotechnology’s unclear journal-set boundaries with biotechnology’s more discrete journal set.
- Research gap: Prior analyses traced deviant being-cited patterns but did not show that these patterns also indicated new developments.The paper identifies this unresolved issue as a limitation of earlier interdisciplinarity indicators.
- Research gap: The paper argues that an interdisciplinarity indicator for individual journals is needed before groups of journals in interdisciplinary fields can be delineated.The motivating question is how journal articles draw upon or feed into different intellectual traditions.
2. Centrality Measures in Social Network Analysis
Social network analysis offers centrality measures for locating journals within citation networks. The paper distinguishes betweenness as an interface-oriented measure from closeness and degree measures.
- Degree centrality: Degree centrality counts a node’s relations, which can be separated into incoming and outgoing connections.In citation matrices, references correspond to outdegree and citations received correspond to indegree.
- Betweenness centrality: Betweenness centrality measures how often a node lies on shortest paths between other nodes in the network.It is based on the proportion of geodesics that include the node under study.
- Closeness centrality: Closeness centrality is computed from a vertex’s distances to all other vertices and provides a global measure of network position.Betweenness is instead defined with reference to a vertex’s local position.
- Betweenness centrality: A journal positioned between dense groups may relate those groups without belonging to one of them.The paper presents this relational position as distinct from factor-loading interpretations that depend on the analytic model.
- Interpretive distinction: Within a set, closeness may indicate multidisciplinarity, whereas betweenness may indicate specific interdisciplinarity at interfaces.The distinction follows from closeness to connected clusters versus a position linking groups.
3. Size, impact, and centrality
Citation-network centrality can be distorted by journal size, so the paper examines betweenness in normalized vector spaces and local citation environments. Its examples show that normalization changes the apparent intermediary position of journals.
- Size and normalization: Large journals can obtain high betweenness centrality because of high degree centrality, creating possible spurious correlations between size and centrality.Normalization of citation-pattern matrices is presented as a way to suppress this effect.
- Normalized citation environment: Among 54 journals citing Social Networks more than once, Social Networks lies on 15% of possible shortest paths, followed by Journal of Mathematical Sociology at 11%.The visual pattern connecting different subgroups matches the expected interpretation of interdisciplinarity.
- Unnormalized citation environment: Before cosine normalization, Social Networks has betweenness 0.07, while Journal of Mathematical Sociology has 0.01 and American Sociological Review 0.03.The larger American Sociological Review is described as having a distinct disciplinary affiliation.
- Size and normalization: Unnormalized citation visualization does not reveal the relevant cluster structure or betweenness among groups of nodes.The paper states that similarity-based normalization is needed to observe latent structures in the citation data.
- Study design: The paper systematically studies betweenness in non-normalized and cosine-normalized matrices before applying the measure to policy-relevant environments including nanotechnology.The research question concerns betweenness centrality in vector space and its applications.
4. Methods and Materials
The study uses 2004 journal citation data to compare centrality measures globally and within local citation environments. It constructs cosine-based vector spaces and analyzes them with Pajek while retaining the asymmetry of citation matrices.
- Data: The dataset combines the Science Citation Index and Social Sciences Citation Index from 2004.The study focuses on cited patterns for comparison with established citation indicators.
- Data: The combined citation matrix represents 7,379 journals after accounting for overlap between the two databases.The source counts 5,968 and 1,712 journals, with 301 covered by both.
- Normalization: The cosine measures the angle between citation-pattern vectors and supports vector-space visualization of sparse citation matrices.Unlike Pearson correlation, it normalizes with reference to the geometrical mean and does not presume normality.
- Normalization: Citation and cosine matrices differ structurally: citation matrices are asymmetric transaction matrices, whereas cosine matrices are symmetric with unity on the diagonal.Their differing topographies motivate treating the two representations separately.
- Citation environments: Local citation impact environments are subsets of journals citing a specific journal, allowing centrality values to be studied within specialized relational contexts.Centrality in a local environment can differ from its value in the global set because paths may involve journals outside the subset.
- Analysis: Centrality calculations use Pajek, focusing on degree, betweenness, and closeness because eigenvector analysis is used there only for visualization.Pajek also analyzes asymmetric matrices in both directions, matching the study’s interest in citation relations.
5. Centrality at the level of the Journal Citation Reports
At the Journal Citation Reports level, centrality measures reveal size, citation impact, and communication reach, but do not by themselves provide a clear interdisciplinarity measure. Betweenness is strongly tied to degree, while closeness cannot be computed in the disconnected citation network.
- Three factors explain 73.5% of variance: size accounts for 46.9%, citation effects for 16.4%, and communication reach for 10.3%.
- Betweenness centrality and indegree overlap substantially, while betweenness and closeness correlate at r = 0.21 (p < 0.01).The other centrality correlations exceed r > 0.5 (p < 0.01).
- Global centrality measures do not discriminate sufficiently to measure interdisciplinarity or multidisciplinarity at the file level.Their interpretation is unclear beyond Science and Nature having the highest centrality, although both measures correlate with impact factor at r = 0.47 (p < 0.01).
- Closeness centrality cannot be computed in the vector space because the network is not fully connected.
- At the global level, betweenness centrality correlates with degree at r = 0.69 (p < 0.01).The top-ten lists for these two indicators share seven journals, with the same order among the top four.
6. The local citation impact environments
The local citation environment of Social Networks reveals how centrality measures distinguish journals’ positions among connected disciplinary clusters. Betweenness identifies bridging roles more specifically than closeness, while interdisciplinarity remains dependent on the selected citation environment.
- 6.1. Social Networks as an example: Social Networks and the Journal of Mathematical Sociology connect clusters spanning sociology, management science, physics, computer science, and statistics.Their contribution to citation impact is only 0.41% and 1.07%, respectively.
- 6.1. Social Networks as an example: The citation-impact visualization represents 54 citing journals, with axes proportional to impact including and excluding within-journal citations.Eleven journals appear as isolates in the network.
- 6.2. Multi- and interdisciplinarity: Betweenness centrality highlights journals interfacing specific clusters and constructing network coherence, with Social Networks and the Journal of Mathematical Sociology especially positioned between clusters.The distribution is more skewed than those of degree and closeness centrality.
- 6.2. Multi- and interdisciplinarity: Betweenness centrality is an effective indicator of interdisciplinarity in local environments, whereas closeness centrality fails as an indicator of multidisciplinarity.Betweenness improves and changes as the journal sets become more coherently defined.
- 6.3. Larger and smaller sets: domain dependency: Social Networks’ interdisciplinarity is 5% in this citation environment, showing that the measure depends on the set of journals used for assessment.The indicator is therefore defined relative to a given citation environment.
7. Further tests and applications
Further tests apply the normalized betweenness measure to Scientometrics, biotechnology, and nanotechnology citation environments. The results show that it distinguishes interface journals and can identify where interdisciplinary development is concentrated.
- 7.1. Scientometrics: The cosine normalization corrects for degree centrality’s effect on betweenness centrality in the vector space.This test addresses the possibility that the seed journal’s high degree centrality could inflate its betweenness.
- 7.1. Scientometrics: In the Scientometrics environment, 24 of 54 journals are disconnected from the core set at cosine ≥ 0.2, indicating incidental citation relations.The remaining graph contains 30 journals.
- 7.1. Scientometrics: Research Policy and Research Evaluation have betweenness centralities of 26% and 25%, respectively, compared with 5% for Scientometrics.The two journals are the interdisciplinary journals identified in this environment.
- 7.2. Biotechnology and Bioengineering: In biotechnology, Biotechnology and Bioengineering lies on only 3% of possible geodesics, while the Biochemical Engineering Journal reaches 6%.The findings place the focus of interdisciplinary development on the engineering side of biotechnology.
- 7.3. Nano Letters: The betweenness measure places Nano Letters among journals occupying an interdisciplinary position between surrounding chemistry and physics journals.The result identifies an interface within an emerging nanoscience and nanotechnology field.
- 7.3. Nano Letters: In the Nano Letters environment, the Journal of Nanoscience and Nanotechnology has 7% betweenness centrality versus 4% for Nano Letters.Its impact factor is 2.017 and total citation rate 489, both lower than Nano Letters’ corresponding values.
8. Conclusions
The study concludes that normalized betweenness centrality can indicate journal interdisciplinarity in local citation environments, whereas closeness centrality does not reliably measure multidisciplinarity. The measure is domain-specific, sensitive to network construction, and supported by applications across citation environments.
- Betweenness centrality emerged as a possible indicator of journal interdisciplinarity, especially at interfaces between fields.
- The interdisciplinarity measure uses a symmetrical cosine matrix rather than the asymmetrical citation matrix used for conventional centrality measures.Cosine normalization controls for the influence of journal size and degree centrality.
- Closeness centrality could not be substantiated as an indicator of multidisciplinarity because it remains a global measure and loses discriminatory power in tightly connected local contexts.Multidisciplinarity is defined here as publishing work from different disciplinary backgrounds without necessarily integrating them.
- In the Social Networks citation environment, the selected seed journal was decisive for centrality in the cited dimension, while other journals became primary in reconstructing the citing structure.
- Restricting the analysis to Social Sciences Citation Index journals showed that the betweenness measure is domain-specific, while further applications demonstrated its discriminating power.
- The approach can be applied directly to cosine-value matrices and visualized with Pajek, with a cosine threshold of ≥ 0.2 used before betweenness computation.The threshold is described as arbitrary but sufficiently low to retain important connections because the algorithm binarizes the matrix.