Bibliographic coupling edges, weighted by the Vladutz-Cook formula

The first coupling measure that weights shared references by their rarity, proposed by (Vladutz and Cook 1984) and reported by (Shen et al. 2019) (their Eq. 6). It is the ancestor of coupling_strength(), which (Shen et al. 2019) present as a correction of it based on the probabilistic interpretation of the inverse document frequency.

Usage

coupling_vladutz(
  dt,
  source,
  ref,
  weight_threshold = 1,
  output_in_character = TRUE
)

Arguments

dt: A data frame or a data.table of direct citations, one row per link between a citing document and a cited reference. It is not modified.
source: Character scalar. The column of the citing documents: they are the nodes of the coupling network.
ref: Character scalar. The column of the cited references.
weight_threshold: Number. The minimum number of shared references for two documents to be linked (1 by default: any shared reference creates a tie). A threshold of 2 or 3 is common in large corpora, where sharing a single reference is weak evidence of proximity and produces very dense networks. It applies to the number of shared references, not to the normalised weight.
output_in_character: Logical. If TRUE (default), the identifiers are also returned as character columns from and to, to build a tidygraph graph more easily.

Value

A data.table with one row per pair of documents sharing at least weight_threshold references: from and to (character if output_in_character = TRUE), the weight and the original identifiers in Source and Target. Each pair appears once, with Source < Target.

Details

Write $f_j$ for the number of documents citing reference $j$ and $L(A)$ for the length of the bibliography of $A$.

$$w_{AB} = \frac{4}{L(A) + L(B)} \sum_{j \in R(A) \cap R(B)} \frac{1}{f_j}$$

The factor 4 is a normalisation that changes no ranking. It makes the weight reach 1 for two documents with identical bibliographies made of references each cited by exactly two documents; since shared references have $f_j \geq 2$, the weight is never above 1. Computing choices: see coupling_strength().

Why use it in research

It is provided mainly for comparison and replication: it also discounts the references cited by many documents, but the weight of a reference decreases as $1/f_j$ instead of $\log(N/f_j)$, so that it almost ignores all the references except the rarest ones. In the corpus of (Shen et al. 2019) it differs markedly from the other measures (correlations of about 0.6 to 0.7 with the relative coupling, the coupling angle, the coupling strength and the similarity). Use compute_couplings() and correlate_weights() to see how much it matters on your corpus.

Intuition

A shared reference counts for the inverse of the number of documents that cite it: a reference shared by two documents and cited by nobody else counts $1/2$, one cited by a hundred documents counts $1/100$. This is a very steep discount: the measure is almost entirely driven by the rarest references. The sum is then divided by the average length of the two bibliographies (the factor 4 is a convenient scaling). Compare with coupling_strength(), whose discount (a logarithm) is much gentler.

References

Shen S, Zhu D, Rousseau R, Su X, Wang D (2019). “A Refined Method for Computing Bibliographic Coupling Strengths.” Journal of Informetrics, 13(2), 605–615. https://linkinghub.elsevier.com/retrieve/pii/S1751157716300244.

Vladutz G, Cook J (1984). “Bibliographic Coupling and Subject Relatedness.” Proceedings of the American Society for Information Science, 21, 204–207.

Examples

library(biblionetwork)
toy <- data.frame(doc = c("d1", "d1", "d1", "d2", "d2", "d3", "d3", "d4", "d4"),
                  ref = c("r1", "r2", "r3", "r1", "r2", "r3", "r4", "r4", "r5"))
coupling_vladutz(toy, source = "doc", ref = "ref")
#>      from     to weight Source Target
#>    <char> <char>  <num> <char> <char>
#> 1:     d1     d2    0.8     d1     d2
#> 2:     d1     d3    0.4     d1     d3
#> 3:     d3     d4    0.5     d3     d4