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Visualizing Bibliometric Networks

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Measuring Scholarly Impact

Abstract

This chapter provides an introduction to the topic of visualizing bibliometric networks. First, the most commonly studied types of bibliometric networks (i.e., citation, co-citation, bibliographic coupling, keyword co-occurrence, and coauthorship networks) are discussed, and three popular visualization approaches (i.e., distance-based, graph-based, and timeline-based approaches) are distinguished. Next, an overview is given of a number of software tools that can be used for visualizing bibliometric networks. In the second part of the chapter, the focus is specifically on two software tools: VOSviewer and CitNetExplorer. The techniques used by these tools to construct, analyze, and visualize bibliometric networks are discussed. In addition, tutorials are offered that demonstrate in a step-by-step manner how both tools can be used. Finally, the chapter concludes with a discussion of the limitations and the proper use of bibliometric network visualizations and with a summary of some ongoing and future developments.

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Notes

  1. 1.

    The data collection took place on November 7, 2013.

  2. 2.

    To improve the visualization, the Size variation parameter in the Options dialog box has been set to a value of 0.40. In addition, the No. of lines parameter has been set to a value of 500. This has the effect that 500 lines, representing the 500 strongest co-citation relations between journals, are displayed in the visualization.

  3. 3.

    The resolution parameter of VOSviewer’s clustering technique is set to its default value of 1.00, not to the value of 0.50 that was used in the case of the author bibliographic coupling network.

  4. 4.

    To improve the visualization, the Size variation parameter in the Options dialog box has been set to a value of 0.40. A few terms in the upper part of the visualization are not visible in Fig. 13.6.

  5. 5.

    Notice that in the visualization shown in Fig. 13.9, publications are displayed in green rather than in gray. This is because the publications included in the visualization all belong to the same cluster identified by CitNetExplorer’s clustering technique.

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Acknowledgment

We would like to thank Katy Börner and Ismael Rafols for their very helpful comments on an earlier draft of this chapter.

Author information

Authors and Affiliations

  1. Centre for Science and Technology Studies, Leiden University, Leiden, The Netherlands

    Nees Jan van Eck & Ludo Waltman

Authors
  1. Nees Jan van Eck
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  2. Ludo Waltman
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Corresponding author

Correspondence to Nees Jan van Eck .

Editor information

Editors and Affiliations

  1. School of Informatics and Computing, Indiana University, Bloomington, Indiana, USA

    Ying Ding

  2. University of Antwerp, Antwerp, Belgium

    Ronald Rousseau

  3. University of Wisconsin-Milwaukee, Milwaukee, Wisconsin, USA

    Dietmar Wolfram

Appendix: Normalization, Mapping, and Clustering Techniques Used by VOSviewer

Appendix: Normalization, Mapping, and Clustering Techniques Used by VOSviewer

In this appendix, we provide a more detailed description of the normalization, mapping, and clustering techniques used by VOSviewer.

1.1 Normalization

We first discuss the association strength normalization (Van Eck & Waltman, 2009) used by VOSviewer to normalize for differences between nodes in the number of edges they have to other nodes. Let a ij denote the weight of the edge between nodes i and j, where a ij  = 0 if there is no edge between the two nodes. Since VOSviewer treats all networks as undirected, we always have a ij  = a ji . The association strength normalization constructs a normalized network in which the weight of the edge between nodes i and j is given by

$$ {s}_{ij}=\frac{2m{a}_{ij}}{k_i{k}_j}, $$
(1)

where k i (k j ) denotes the total weight of all edges of node i (node j) and m denotes the total weight of all edges in the network. In mathematical terms,

$$ {k}_i={\displaystyle \sum_j{a}_{ij}}\kern1em \mathrm{and}\kern1em m=\frac{1}{2}{\displaystyle \sum_i{k}_i}. $$
(2)

We sometimes refer to s ij as the similarity of nodes i and j. For an extensive discussion of the rationale of the association strength normalization, we refer to Van Eck and Waltman (2009).

1.2 Mapping

We now consider the VOS mapping technique used by VOSviewer to position the nodes in the network in a two-dimensional space. The VOS mapping technique minimizes the function

$$ V\left({\mathbf{x}}_1,\dots, {\mathbf{x}}_n\right)={\displaystyle \sum_{i<j}{s}_{ij}{\left\Vert {\mathbf{x}}_i-{\mathbf{x}}_j\right\Vert}^2} $$
(3)

subject to the constraint

$$ \frac{2}{n\left(n-1\right)}{\displaystyle \sum_{i<j}\left\Vert {\mathbf{x}}_i-{\mathbf{x}}_j\right\Vert }=1, $$
(4)

where n denotes the number of nodes in a network, x i denotes the location of node i in a two-dimensional space, and ||x i  − x j || denotes the Euclidean distances between nodes i and j. VOSviewer uses a variant of the SMACOF algorithm (e.g., Borg & Groenen, 2005) to minimize (3) subject to (4). We refer to Van Eck et al. (2010) for a more extensive discussion of the VOS mapping technique, including a comparison with multidimensional scaling.

1.3 Clustering

Finally, we discuss the clustering technique used by VOSviewer. Nodes are assigned to clusters by maximizing the function

$$ V\left({c}_1,\dots, {c}_n\right)={\displaystyle \sum_{i<j}\delta \left({c}_i,{c}_j\right)\left({s}_{ij}-\gamma \right)}, $$
(5)

where c i denotes the cluster to which node i is assigned, δ(c i , c j ) denotes a function that equals 1 if c i  = c j and 0 otherwise, and γ denotes a resolution parameter that determines the level of detail of the clustering. The higher the value of γ, the larger the number of clusters that will be obtained. The function in (5) is a variant of the modularity function introduced by Newman and Girvan (2004) and Newman (2004) for clustering the nodes in a network. There is also an interesting mathematical relationship between on the one hand the problem of minimizing (3) subject to (4) and on the other hand the problem of maximizing (5). Because of this relationship, the mapping and clustering techniques used by VOSviewer constitute a unified approach to mapping and clustering the nodes in a network. We refer to Waltman et al. (2010) for more details. We further note that VOSviewer uses the recently introduced smart local moving algorithm (Waltman & Van Eck, 2013) to maximize (5).

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van Eck, N.J., Waltman, L. (2014). Visualizing Bibliometric Networks. In: Ding, Y., Rousseau, R., Wolfram, D. (eds) Measuring Scholarly Impact. Springer, Cham. https://doi.org/10.1007/978-3-319-10377-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-10377-8_13

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