Metrics
Citation Depth / Breadth / Dependence / Independence
Citation Depth / Breadth / Dependence / Independence is a multi-dimensional citation impact framework conceptualized by Yi Bu, Ludo Waltman, and Yong Huang in their research paper (Bu, Waltman, and Huang, 2021).
a. Citation Depth/Breadth
To illustrate deep and broad citation impact, consider two publications, A and B. As shown in Figure 1, the two publications each received five citations.
However, the publications citing A also cite each other, and we say that publication A has a deep citation impact because the publications by which it is cited also cite each other, suggesting that these publications all belong to a relatively narrow research area in which they build cumulatively build on each other.
In contrast, the publications citing B do not cite each other, and we say that publication B has a broad citation impact because it is cited by publications that do not cite each other, suggesting that they do not seem to build on each other and they may cover a relatively wide research area.
Figure 1. Deep and broad citation impact [1].
To quantify the depth and breadth of the citation impact of a publication, we deploy the following two indicators (Citation Breadth, and Citation Depth).
| Citations | Absolute Value | Relative Value |
|---|---|---|
| Citation Breadth | The number of publications citing the focal publication that do not cite other publications citing the focal publication | The proportion of publications citing the focal publication that do not cite other publications citing the focal publication |
| Citation Depth | The number of publications citing the focal publication that also cite other publications citing the focal publication | The proportion of publications citing the focal publication that also cite other publications citing the focal publication |
b. Citation Dependence/Independence
To illustrate dependent and independent citation impact, again consider two publications, A and B. As shown in Figure 2, publications A and B have received five citations and have three references.
All publications citing A also cite each of A's references, while the publications citing B do not cite B's references. Hence, the citation impact of A seems to depend strongly on earlier publications, namely those cited by A. A is likely a follow-up study of these earlier publications.
In contrast, B seems to have a much more independent citation impact, as publications citing B do not cite the references of B.
Figure 2. Dependent and Independent Citation Impact [1].
To quantify the dependence and independence of the citation impact of a publication, we deploy the following two indicators (Citation Dependence, and Citation Independence). as illustrated in Table 2.
| Citations | Absolute Value | Relative Value |
|---|---|---|
| Citation Breadth | The number of publications citing the focal publication that also cite references of the focal publication | The proportion of publications citing the focal publication that also cite references of the focal publication |
| Citation Depth | The number of publications citing the focal publication that do not cite references of the focal publication | The proportion of publications citing the focal publication that do not cite references of the focal publication |
This set of indicators evaluates a publication's citation impact more comprehensively. Publications with a deep citation impact are likely to have more impact in a relatively narrow research area, and publications with a broad citation impact probably cover a wider area of research. It also distinguishes between publications strongly dependent on earlier work and publications making a more independent scientific contribution. Note: this set of metrics is now only calculated for the Top Cited Papers, which have a minimum of 100 total citations.
Reference
[1] Bu, Y.; Waltman, L.; Huang, Y. A multidimensional framework for characterizing the citation impact of scientific publications. Quant. Sci. Stud. 2021, 2, 155-183, A multidimensional framework for characterizing the citation impact of scientific publications
Monthly Citation Metric
Number of citations in the past 12 months to publications published in the previous 24 months / number of publications in the previous 24 months (this metric is released monthly, on the 15th day of every month).
h5_index
A journal metric that shows the number of articles published in the last five years that received at least one citation in the same period.
h_index and i10_index
The h_index is a scholar metric calculated by counting the number of publications for which an author has been cited by other authors at least that same number of times.
i10_index is a scholar metric that shows the number of publications with at least 10 citations.
Collaboration Indicator
International collaboration; domestic inter-organizational collaboration; domestic intra-organizational collaboration; single authorship (no collaboration).
The collaboration indicator provides a quantitative measure of the degree of collaboration by examining the collaboration experiences between researchers from different countries.
By systematically analyzing and quantifying collaboration patterns, this indicator provides valuable insights into the dynamics and trends of international collaboration.
Calculation method
First, we tag each article in the Scilit database as one of the following five types.
- 1
International cooperation
An article is written by authors from different countries.
- 2
Domestic inter-organizational collaboration
An article written by authors from the same country but different institutions.
- 3
Domestic intra-organizational collaboration
An article written by authors from the same country and institution.
- 4
Single authorship (no collaboration)
The article has only one author.
- 5
Missing data
No data collected.
Then, we calculate the ratio of a journal / scholar / publisher / organization's documents signed by researchers from more than one country, including more than one country address, as the international collaboration chart shows.