Bibliographic coupling edges, weighted by the coupling angle

Builds the edges of a bibliographic coupling network from a table of direct citations (one row per citing document and cited reference). Two documents are coupled when their bibliographies overlap (Kessler 1963) , and the weight of the tie is the coupling angle (Sen and Gan 1983) : the number of shared references divided by the geometric mean of the lengths of the two bibliographies (a cosine).

Usage

coupling_angle(
  dt,
  source,
  ref,
  normalized_weight_only = TRUE,
  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.
normalized_weight_only: Logical. If FALSE, the number of shared references is returned in addition to the normalised weight.
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: the identifiers in from and to (if output_in_character = TRUE), the weight (coupling angle) and, if normalized_weight_only = FALSE, nb_shared_references. The original identifiers are kept in Source and Target (from and to are modified by tidygraph when a graph is created). The network is undirected: each pair appears once, with Source < Target.

Details

Write $R(A)$ for the set of references of document $A$, and $L(A) = |R(A)|$ for the length of its bibliography. The weight of the tie between $A$ and $B$ is

$$w_{AB} = \frac{|R(A) \cap R(B)|}{\sqrt{L(A) \, L(B)}}$$

The numerator is the number of shared references (returned as nb_shared_references when normalized_weight_only = FALSE). Dividing by $\sqrt{L(A) L(B)}$ avoids giving too much importance to documents with a long bibliography, such as literature reviews. The weight lies between 0 and 1, and is 1 only if the two bibliographies are identical.

The function applies the following rules, which matter for the interpretation of the result:

duplicated rows are counted once, and a document citing itself is ignored;
$L(A)$ counts all the references of $A$, including those cited by no other document of the table. Such references cannot create a tie but they lengthen the bibliography, and so lower the weights of $A$;
rows with a missing identifier are dropped, with a warning;
the table of the user is not modified;
if no reference is shared by two documents (or if no pair reaches weight_threshold), a zero-row table is returned, with the usual columns, and a warning that says why.

The function is written with data.table and is fast, but it first lists every pair of documents citing a same reference: a reference cited by $n$ documents creates $n (n - 1) / 2$ pairs. Very popular references (a classic cited by tens of thousands of documents) may therefore exhaust the memory on a large corpus. Split the corpus (by time window, for instance), or remove the most cited references, before calling the function.

The function is general: it only needs two columns of identifiers. With source the articles and ref the words of their titles, it builds a title co-occurrence network; with source the cited documents and ref the citing ones, a co-citation network (but see biblio_cocitation()).

Why use it in research

Documents that cite the same references rely on the same literature: they are likely to address related questions, with related tools. Bibliographic coupling is therefore a standard way of mapping the research fronts of a field, and to group documents into specialities or schools with a community detection algorithm (Boyack et al. 2005; Boyack and Klavans 2010; Yan and Ding 2012) . Two properties make it convenient for the history and sociology of science:

the links are fixed when a document is published, since they depend only on its own bibliography. A network built for 1970-1979 does not change when later documents are added, which allows comparing successive time windows (a dynamic analysis);
it covers all the documents of the corpus, even uncited ones, as long as their references are recorded.

Its limit is the quality of the reference lists: documents without recorded references cannot be linked. Compare with the co-citation approach, which links cited documents and changes as new citations accumulate, and with the measures that weight the shared references (coupling_strength(), coupling_similarity()).

Intuition

Picture each bibliography as a shopping list. Two lists that contain many of the same items are probably written by people who shop for the same meal. But a very long list contains many items by sheer size, and would look similar to everybody: the weight therefore compares the shared items with the geometric mean of the lengths of the two lists. Geometrically, each document is an arrow in a space with one axis per reference, pointing along the axes of the references it cites; the weight is the cosine of the angle between two arrows (hence "coupling angle"): 1 for identical bibliographies (same direction), 0 for bibliographies with nothing in common (perpendicular).

References

Boyack KW, Klavans R (2010). “Co-Citation Analysis, Bibliographic Coupling, and Direct Citation: Which Citation Approach Represents the Research Front Most Accurately?” Journal of the American Society for Information Science and Technology, 61(12), 2389–2404. doi:10.1002/asi.21419 .

Boyack KW, Klavans R, Börner K (2005). “Mapping the Backbone of Science.” Scientometrics, 64(3), 351–374. doi:10.1007/s11192-005-0255-6 .

Kessler MM (1963). “Bibliographic Coupling between Scientific Papers.” American Documentation, 14(1), 10–25. doi:10.1002/asi.5090140103 .

Sen SK, Gan SK (1983). “A Mathematical Extension of the Idea of Bibliographic Coupling and Its Applications.” Annals of library science and documentation, 30(2).

Yan E, Ding Y (2012). “Scholarly Network Similarities: How Bibliographic Coupling Networks, Citation Networks, Cocitation Networks, Topical Networks, Coauthorship Networks, and Coword Networks Relate to Each Other.” Journal of the American Society for Information Science and Technology, 63(7), 1313–1326. doi:10.1002/asi.22680 .

Examples

library(biblionetwork)
# Edges between the documents explaining the 1970s stagflation, keeping
# the pairs that share at least three references
edges <- coupling_angle(Ref_stagflation,
                         source = "Citing_ItemID_Ref",
                         ref = "ItemID_Ref",
                         weight_threshold = 3)
head(edges)
#>       from       to     weight  Source   Target
#>     <char>   <char>      <num>   <int>    <int>
#> 1:  214927  2207578 0.14605935  214927  2207578
#> 2: 5160307  6714008 0.09128709 5160307  6714008
#> 3: 1717556  7815498 0.16564729 1717556  7815498
#> 4:  214927  8456979 0.09733285  214927  8456979
#> 5: 2207578  8456979 0.11846978 2207578  8456979
#> 6: 5240516 10585974 0.14726421 5240516 10585974

# A tiny example that can be checked by hand: d1 and d2 share two of
# their (respectively 3 and 2) references, so the weight is 2 / sqrt(3 * 2)
toy <- data.frame(doc = c("d1", "d1", "d1", "d2", "d2"),
                  ref = c("r1", "r2", "r3", "r1", "r2"))
coupling_angle(toy, source = "doc", ref = "ref", normalized_weight_only = FALSE)
#>      from     to    weight nb_shared_references Source Target
#>    <char> <char>     <num>                <int> <char> <char>
#> 1:     d1     d2 0.8164966                    2     d1     d2