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BY 4.0 license Open Access Published by De Gruyter Open Access July 31, 2023

Adding Perspective to the Bibliometric Mapping Using Bidirected Graph

  • Faizhal Arif Santosa EMAIL logo
From the journal Open Information Science


Bibliometric mapping offers easiness in analyzing the relationship between publications through the network visuals created. Several applications, such as VOSviewer, Bibliometrix, and CiteSpace, make conducting network analysis more convenient. Moreover, the relationship provided is usually in the form of an undirected graph, which negates the two-way relationship created. This study attempts to demonstrate the significance of considering two-way relationships by proposing a keyword network formed using bidirected graphs and association rules to examine the two-way relationship of two or more keywords. According to the proposed bidirected graph, a two-way graph can add value and insight by analyzing the correlation between a single keyword and several others. Two of the four metrics used, Confidence and Conviction, are sufficient to support directed graphs. In contrast, Support and Full Counting are related because they both see the occurrences of a keyword, so using undirected graphs is necessary.

1 Introduction

Bibliometrics is widely recognized as a tool for analyzing patterns in a bibliographical collection. With common techniques such as citation analysis, co-citation analysis, bibliographic coupling analysis, co-word analysis, and co-authorship analysis, bibliometric analysis is an emerging method for synthesizing research that focuses on the bibliographic information (Gan, Li, Robinson, & Liu, 2022). Several applications available provide the convenience of conducting bibliometric analysis that can be done independently or as a service by some libraries. VOSviewer, Bibliometrix, CiteSpace, SciMat, and Sci2 Tool, for example, are software that enable users to create maps based on network data and then visualize and explore those maps.

Mapping of networks visualizes multiple items (e.g., authors, journals, or keywords), and an edge represents a relationship between two items (Waaijer & Palmblad, 2015). This suggests that there is a unified relationship between the two keywords without regard to how keyword A perceives keyword B and vice versa. The study conducted by Li (2017) showed that keyword relationships can vary depending on the metrics used. This demonstrates that if any other measurement is used, another line that examines the relationship of each item must be considered.

2 Literature Review

2.1 Bibliometric Mapping

Bibliometric mapping is the spatial display of relationships between different fields of study, specific works, authors, or other entities (Small, 1999). This is a method of visualizing different types of literature structures in order to provide insight for developing studies and identifying gaps (Donthu, Kumar, Mukherjee, Pandey, & Lim, 2021; José de Oliveira, Francisco da Silva, Juliani, César Ferreira Motta Barbosa, & Vieira Nunhes, 2019). When the data are so large that it is difficult to analyze manually, using the visualization created will make it easier to do relationship analysis.

Co-word analysis, which investigates current or potential relationships between topics with a focus on the written content of the publication, is one of the key methods used in bibliometric analysis (Donthu et al., 2021). When describing the emergence of multidisciplinary fields that combine more complex knowledge, the network map based on co-word analysis is particularly suitable because it represents the search topics of a particular discipline (Wang, Zhu, Song, Hou, & Zhang, 2018). Co-word analysis can shed light on common research focuses and pertinent research trends, aiding discussions and suggesting new research directions (Donthu et al., 2021; Lin, Tang, Lin, Changlai, & Hsu, 2022). It will be simpler to comprehend and gather information from the relationships that are created between one another through the networks that are formed, such as keywords or authors.

It is now easier to create a network map by utilizing various software programs, such as VOSviewer, Bibliometrix, and CiteSpace. VOSviewer creates a network visualization by connecting each item with lines of varying thicknesses based on the strength of the links (van Eck & Waltman, 2022). Meanwhile, Bibliometrix also plots networks created with networkPlot using VOSviewer by Nees Jan van Eck and Ludo Waltman (Aria & Cuccurullo, 2017). On the other hand, on CiteSpace, a line linking two items in the visualization denotes a co-citation link, and the thickness of a line on the timeline visualization is proportionate to the strength of co-citation (Chen, Ibekwe-SanJuan, & Hou, 2010). The relationship lines formed by each item are represented as undirected graph lines. “Undirected” have undirected edges, whereas directed graphs have directed edges (Concas, Fenu, Reichel, Rodriguez, & Zhang, 2022). It is also worth noting that between points x and y, two vertices from and to that point can exist (Wasserman, 1975).

In general, the undirected graph is used to see the relationship between one keyword and another, so the relationship is displayed as a line on an undirected graph. Because the direction of a relationship is less important and easier to define, undirected graphs are commonly used (Mehlhorn & Sanders, 2008). However, it’s frequently necessary to consider a relationship from two angles. The various relationships from and to a point can be observed through the multigraph that Edmonds and Johnson (2003) introduced as a bidirected graph. Bidirected graph defines the existence of a line connecting one point to another and vice versa (Mehlhorn & Sanders, 2008). This is especially useful when a relationship xy is different from yx.

2.2 Another Metrics Approach

To identify relationships in large transaction datasets, researchers in academia and industry, particularly in the marketing field, use an algorithm known as association rules (ARs) (Tatiana & Mikhail, 2018). Furthermore, AR can be used in text mining (Lopes, Pinho, Paulovich, & Minghim, 2007). Support and Confidence are commonly used to measure relationship formed in AR, while the strength of the relationship can be seen in Lift, where the stronger the relationship, the higher the value of Lift (Jibril, Kwarteng, Appiah-Nimo, & Pilik, 2019; Tatiana & Mikhail, 2018). The formula for these three measurements is shown in (1) Support, (2) Confidence, and (3) Lift. Through the Confidence value, AR recognizes that the relationship that results from xy may differ from yx.

(1) Support ( x y ) = Document containing x and y Total documents ,

(2) Confidence ( x y ) = Document containing x and y Document containing x ,

(3) Lift ( x y ) = Support Support ( x ) * Support ( y ) .

The use of AR in co-word analysis was introduced by Li (2017) and Li and Chu (2017) by utilizing burst word detection under the name AR mining between keywords and burst words (ARM-KB). The ARM-KB uses three commonly used measures: Confidence, Support, and Lift. On the other hand, Brin, Motwani, Ullman, and Tsur (1997) propose the value of Conviction, which is useful for overcoming the limitations of measures of “interestingness” such as Confidence and Lift, and is truly a measure of implication because it is directed and maximal for perfect implications. Conviction compares the probability that x occurs without y if they depend on the actual frequency of occurrence of x without y (Prajapati, Garg, & Chauhan, 2017). Conviction value is calculated using equation (4).

(4) Conviction ( x y ) = 1 Support ( y ) 1 Confidence ( x y ) .

The calculations provided by several other applications in forming knowledge maps are limited to an entity (author or word) with another entity, making it difficult to determine the relationship between one and many entities. VOSviewer provides two types of calculations for establishing relationships between entities: Full Counting and Fractional Counting. While Full Counting provides a total for each document, Fractional Counting provides a 1/n formula where n is the number of co-authors/keywords (van Eck & Waltman, 2022). On the other hand, in order to find frequent item sets, AR learning involves the occurrence of various items and provides a set of frequent items along with rules that were generated based on the given items (Iqbal et al., 2022). By adjusting the number of itemsets, seeing the relationship between one keyword to many keywords is very possible by using AR.

This article attempts to compare the bibliometric mappings produced in co-word analysis using VOSviewer and bidirected graphs. Further exploration was also carried out to see if there were differences or similarities in the calculations produced by these two methods. In addition, the relationship from one to many keywords will be explored further in this study.

3 Method

This study used 141 data entries from the Journal of Data and Information Science from 2018 to 2022 taken from Scopus. The data used in this study are in the form of author keywords, which were used to determine the relationship of keywords to one another. Keyword identification is made to find out similar keywords using lemmatization. By employing the lemmatization approach, the words used will be able to identify their basic form (Korenius, Laurikkala, Järvelin, & Juhola, 2004). Because some keywords may have the same meaning but in different forms, keyword cleaning is required (Gan et al., 2022; Santosa, 2023). The WordNet Lemmatizer from the Natural Language Toolkit was utilized in this study. Furthermore, because 12 entries lacked author keywords, only 129 were processed further.

In this study, FP-Growth is used to generate itemsets, which is known to be capable of generating frequent itemsets without generating candidates (Naresh & Suguna, 2019). Additionally, FP-Growth can perform better than pattern generation-based algorithms in terms of performance (Han, Pei, Yin, & Mao, 2004). This study established a Support value of 0.01 and a Confidence value of 0.21. The maximum number of itemsets that can be generated is set at 3, which allows seeing the relationship between numerous keywords. Furthermore, this research uses the Python library Mlxtend (machine learning extensions) to construct FP-Growth to extract frequent itemsets for AR on keywords. Visualizations are made using the Python library Streamlit Agraph, where each node represents a collection of itemsets (a single keyword or a group of keywords). Meanwhile, on the VOSviewer side, Full Counting and Fractional Counting were performed on author keywords using the co-occurrence analysis type.

4 Result and Discussion

As a result of the cleaning of the data, the original 533 keywords were reduced to 523 keywords. Some words were combined such as [Citation context] and [Citation contexts], [Research information system] and [Research information systems], and [Universities] and [University]. However, because this process failed to detect [scientometric] and [scientometrics], [performance-based funding] and [performance based funding], and [Performance-based Research Funding System] and [Performance-based Research Funding System (PRFSs)], changes had to be made manually. Apart from the instances where it encountered problems with synonyms and polysemies, this demonstrates the inadequacy of lemmatization. Keyword expansion is one method considered to address this issue (Ayetiran, 2020) or using other applications such as OpenRefine for maximum results. The top five keywords were bibliometrics, scientometrics, research evaluation, Norwegian model, and Twitter.

Both methods can display network visualizations with varying calculations. As shown in Figure 1, the network provided a single line of relationship between two points that VOSviewer produces. As a result of the AR-generated networks shown in Figure 2, two lines with a two-way relationship were produced. Different information is contained in each formed line. AR-generated networks can be chosen based on their Support or Confidence value. The two bibliometric maps also show that four of the five most popular keywords have a direct relationship and form a network group, whereas the Twitter keywords do not have a direct relationship and form their own network.

Figure 1 
               VOSviewer’s network visualization.
Figure 1

VOSviewer’s network visualization.

Figure 2 
               Bidirected graphs utilizing AR.
Figure 2

Bidirected graphs utilizing AR.

The difference occurs in the relationship between bibliometrics and the top three keywords (scientometrics, research evaluation, and Norwegian model). In VOSviewer, the resulting maps take the form of undirected graphs, with a connecting line for each keyword that has a relationship (Figure 1). While it can be seen in the bidirected graphs that these three keywords have lines that all point to bibliometrics, there is a missing link from bibliometrics to these three keywords (Figure 2). This occurs because the observed relationship does not meet the specified initial parameters because the resulting Confidence value is 0.18, which is less than the specified threshold of 0.21. It also appears that some nodes have two relationship lines, indicating that the relationship between nodes meets the value with the specified parameters.

With predefined parameters, AR generated as many as 33 relationships where 11 of them are relationships between single keywords and multiple keywords (Appendix). By adjusting the maximum number of itemsets generated, relationships between one and many keywords can also be created. While VOSviewer was unable to view one-to-many relationships, AR can give users a broad overview of the relationship values between different keywords. Using the resulting Antecedent and Consequent Support values, it appears that [bibliometrics, performance-based funding] and [performance-based funding, Norwegian model], with a value of 0.023, are the paired keywords that frequently appear. Both bibliometrics with performance-based funding and Norwegian model with performance-based funding have a Full Counting value of 3 and are the highest compared to other relationships when expressed through a one-to-one relationship. Apart from the fact that these two calculations depend on occurrences in data, this is what makes the relationship between the two keywords in VOSviewer comparable to the value of the Support keywords in pairs.

Full Counting was directly related to Support value of the 33 rule examples used. This is so because calculating the frequency is a fundamental component of both calculation models. The four relationships in numbers 14–17, as shown in Appendix, have the highest Full Counting and Support values. It can also be concluded that the Support value can be used to define link strength from one relationship to many keywords. Meanwhile, the value of Support does not differ between the relationships xy and yx, so using bidirected graphs to analyze the emergence of a keyword relationship is less precise.

At the same time, the lowest Confidence value is 0.250, and 11 relationships have a maximum value of 1. When Antecedents and Consequents switch positions, numbers 3–4 and 7–8 show the same perfect score, implying that [university, ranking] are interdependent and appear in the same document as [development of data and information services, higher education institution]. The Confidence value also has an impact on one-to-many relationships, such as [research information system] and Consequents [performance-based funding], [Norwegian model], and [performance-based funding, Norwegian model], where the one-to-one relationship in numbers 25–26 has the same value as 32.

The Confidence value, an useful metric to show the strength of the implications (Stit, Riffi, Yahyaouy, & Tairi, 2018), demonstrates what sets the relationship apart from xy and yx. For instance, [social medium] → [Twitter] has a value of 0.667, indicating that [social medium] is more frequently found in documents containing both keywords than [Twitter], which has a lower value of 0.40. Some keywords only have one line due to the difference in the relationship that Confidence displays because the resulting value does not meet the required threshold. Given that it will be challenging to distinguish different values from the relationship between the same two keywords using undirected graphs, it can be concluded that bidirected graphs are necessary to see this metric.

Lift refers to the potential influence of Antecedent keywords on the occurrence of Consequent keywords (Li & Chu, 2017). Additionally, the value of Lift is equal to one if there is no dependence between the items (Iqbal et al., 2022). There is no Lift value that is worth 1 of all the relationships that appear, and the value of 64.5 is the highest value that appears in numbers 4–5 and 8–9. This occurs because these keywords are always found in pairs in existing documents, allowing the Lift to be used to identify opportunities for topics that have not been exposed to other topics due to the fact that the keywords used are always found in pairs.

Furthermore, the relationship between xy and yx in Lift is constant. Because the component for calculating the Lift in the numerator is Support, which is always the same, and in the denominator it is the multiplication between Support (x) and Support (y), which is reversed, the result will still be the same, the position of the Lift value will remain constant for each keyword exchange. This similar relationship suggests that the use of bidirected graphs will be less advantageous because the lines formed have the same value, making the use of undirected graphs simpler.

The maximum Confidence value for 11 relationships results in an infinity value when using the Conviction metric. In interactions where the same values of Lift and Confidence are present, the value of Conviction will always be the same (Prajapati et al., 2017). The relationship between [scientometrics] toward [bibliometrics] appears to have the lowest value with a value of 1,22 where the probability of appearing randomly is greater when compared to [performance-based funding] toward [Norwegian model] with a value of 3,845 where it can be concluded that this relationship is more likely strong and not a mere coincidence.

Brin et al. (1997) stated that Conviction is a true measure of implication because it is directional. It is very appropriate to use bidirected graphs to visualize the relationship that is formed between the two items in Conviction because, like Confidence, the relationship between the two items in Conviction has the potential to produce different values. But interpreting infinity as a number brings a problem for Conviction. Contrarily, Confidence has a distinct range between 0 and 1, so it will be more appropriate to use Confidence rather than Conviction when attempting to adjust the style of a line, for instance by varying the line’s thickness.

5 Conclusions

This study demonstrated how a bidirected graph using AR could enhance keyword network analysis, particularly in terms of how keywords can support one another. The value of Support can indicate the frequency of occurrence of two keywords in a set of documents. In contrast, Confidence can help assess the presence of two keywords in documents that include one or more of these keywords. The Lift value can also be used as an input to determine the strength of the relationship from existing keywords; the higher the value, the stronger the relationship. On the other hand, there were numerous relationships between keywords that have the highest Lift value. Note that in this study, this can occur if two or more related keywords appear only in a few documents. This case affects the value of this high Lift, so more investigation into the maximum score on the Lift is required. Then, seeing Conviction can provide additional insight into the strength of keywords and how they may appear by coincidence.

Given that both Support value and Full Counting consider the presence of keywords in the data they have, they have a linear relation. The Support and Lift values between the two keywords are monotonous according to the four metrics used, making it simpler to use undirected graphs. However, the other two values, namely Confidence and Conviction, have variable values and view the relationship from two different angles, making the use of bidirected graphs unavoidable. In addition, Conviction has a problem with the infinity value, so variations in line thickness are more likely on Confidence values with definite range.

It is also possible to have one-to-many entity relationships, where the number of keywords is determined by how many itemsets will be produced. The disadvantage of a bidirected graph is that the more data there are, the more complicated the network becomes. In order to make it simpler to understand the relationship that occurs, it is, therefore, necessary to set the parameters used. Using new calculation techniques can add value to using this visualization, so this study is limited to using AR to see metrics that support bidirected graphs. Additionally, metrics that detect the presence of a keyword, like the value of Support, tend to have a smaller value, the larger the dataset used, requiring the derivation of the necessary parameters in order to detect a relationship.

  1. Funding information: The author states that no funding was involved.

  2. Conflict of interest: The author states no conflict of interest.

  3. Data availability statement: Data for this study are available in A web application to visualize is accessible at


No. Antecedents Consequents Full counting Fractional counting Antecedent support Consequent support Support Confidence Lift Conviction
1 Social medium Twitter 2 0.53 0.02325581 0.03876 0.015504 0.667 17.200 2.884
2 Twitter Social medium 2 0.53 0.03875969 0.023256 0.015504 0.400 17.200 1.628
3 Ranking University 2 0.5 0.01550388 0.015504 0.015504 1.000 64.500 Infinity
4 University Ranking 2 0.5 0.01550388 0.015504 0.015504 1.000 64.500 Infinity
5 Scientometrics Bibliometrics 2 0.34 0.0620155 0.085271 0.015504 0.250 2.932 1.220
6 Research management Bibliometrics 2 0.53 0.01550388 0.085271 0.015504 1.000 11.727 Infinity
7 Development of data and information service Higher education institution 2 0.53 0.01550388 0.015504 0.015504 1.000 64.500 Infinity
8 Higher education institution Development of data and information service 2 0.45 0.01550388 0.015504 0.015504 1.000 64.500 Infinity
9 Social network analysis Bibliometrics 2 0.34 0.02325581 0.085271 0.015504 0.667 7.818 2.744
10 h-Index Bibliometrics 2 0.7 0.02325581 0.085271 0.015504 0.667 7.818 2.744
11 Research evaluation Bibliometrics 2 0.48 0.04651163 0.085271 0.015504 0.333 3.909 1.372
12 Performance-based research funding system Norwegian model 2 0.5 0.03100775 0.03876 0.015504 0.500 12.900 1.922
13 Norwegian model Performance-based research funding system 2 0.5 0.03875969 0.031008 0.015504 0.400 12.900 1.615
14 Bibliometrics Performance-based funding 3 0.93 0.08527132 0.031008 0.023256 0.273 8.795 1.332
15 Performance-based funding Bibliometrics 3 0.93 0.03100775 0.085271 0.023256 0.750 8.795 3.659
16 Performance-based funding Norwegian model 3 0.85 0.03100775 0.03876 0.023256 0.750 19.350 3.845
17 Norwegian model Performance-based funding 3 0.85 0.03875969 0.031008 0.023256 0.600 19.350 2.422
18 Bibliometrics, performance-based funding Norwegian model 0.02325581 0.03876 0.015504 0.667 17.200 2.884
19 Bibliometrics, Norwegian model Performance-based funding 0.01550388 0.031008 0.015504 1.000 32.250 Infinity
20 Performance-based funding, Norwegian model Bibliometrics 0.02325581 0.085271 0.015504 0.667 7.818 2.744
21 Performance-based funding Bibliometrics, Norwegian model 0.03100775 0.015504 0.015504 0.500 32.250 1.969
22 Norwegian model Bibliometrics, performance-based funding 0.03875969 0.023256 0.015504 0.400 17.200 1.628
23 Norwegian model Bibliometrics 2 0.6 0.03875969 0.085271 0.015504 0.400 4.691 1.525
24 Performance-based funding Research information system 2 0.35 0.03100775 0.015504 0.015504 0.500 32.250 1.969
25 Research information system Performance-based funding 2 0.35 0.01550388 0.031008 0.015504 1.000 32.250 Infinity
26 Research information system Norwegian model 2 0.35 0.01550388 0.03876 0.015504 1.000 25.800 Infinity
27 Norwegian model Research information system 2 0.35 0.03875969 0.015504 0.015504 0.400 25.800 1.641
28 Performance-based funding, research information system Norwegian model 0.01550388 0.03876 0.015504 1.000 25.800 Infinity
29 Performance-based funding, Norwegian model Research information system 0.02325581 0.015504 0.015504 0.667 43.000 2.953
30 Research information system, Norwegian model Performance-based funding 0.01550388 0.031008 0.015504 1.000 32.250 Infinity
31 Performance-based funding Research information system, Norwegian model 0.03100775 0.015504 0.015504 0.500 32.250 1.969
32 Research information system Performance-based funding, Norwegian model 0.01550388 0.023256 0.015504 1.000 43.000 Infinity
33 Norwegian model Performance-based funding, research information system 0.03875969 0.015504 0.015504 0.400 25.800 1.641


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Received: 2023-04-14
Revised: 2023-06-22
Accepted: 2023-07-06
Published Online: 2023-07-31

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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