This vignette is a guided tour of the functions of biblionetwork, using the data included in the package (see Section 1). Every function turns a table of links between two kinds of items (for instance documents and the references they cite) into the edges of a network whose nodes are one of the two kinds, with a weight for each edge. The functions differ by the kind of nodes and by the way the weight is computed.
| You want to link… | Because they… | Function |
|---|---|---|
| citing documents | share references (Kessler 1963) |
biblio_coupling() (see Section 2) |
| cited references | are cited together (Small 1973) |
biblio_cocitation() (see Section 3) |
| authors, journals, institutions | cite the same references (or are cited together) through their documents (Zhao and Strotmann 2008) |
entity_network() (see Section 4) |
| authors, institutions, countries | co-sign documents |
coauth_network() (see Section 5) |
The data included in the package
The package contains bibliometric data built by Goutsmedt (2021): the academic articles and books, published between 1975 and 2013, that tried to explain the US stagflation of the 1970s, and the references they cite.
-
Ref_stagflationis a table of direct citations: one row per link between a citing document (Citing_ItemID_Ref) and a cited document (ItemID_Ref). It is the typical input of the coupling and co-citation functions. -
Nodes_stagflationdescribes the stagflation documents, and the references cited by at least two of them (one row per document, with the first author only). -
Authors_stagflationlists the stagflation documents with all their authors (one row per author and document). It is the input of the co-authorship function.
Ref_stagflation[1:5, 1:2]#> Citing_ItemID_Ref ItemID_Ref
#> <int> <int>
#> 1: 1111111131 1111111354
#> 2: 20623867 49263876
#> 3: 25850485 72060
#> 4: 16995857 202546
#> 5: 106566088 209143Every function of the package needs only two columns of identifiers, that you name in the arguments source and ref. The names of the columns in your own data do not matter, and the table you give is never modified.
Bibliographic coupling: biblio_coupling()
Two documents are bibliographically coupled when they cite the same references (Kessler 1963): the more their bibliographies overlap, the more likely they are to address related questions. biblio_coupling() takes a table of direct citations and returns the list of the pairs of documents that share at least one reference, with a weight for each pair.
edges <- biblio_coupling(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
normalized_weight_only = FALSE)
edges#> from to weight nb_shared_references Source
#> <char> <char> <num> <int> <int>
#> 1: 1021902 1184127 0.04622502 1 1021902
#> 2: 214927 2207578 0.14605935 4 214927
#> 3: 1184127 2901822 0.04233338 1 1184127
#> 4: 1184130 2901822 0.05184758 1 1184130
#> 5: 1717556 2901822 0.02804964 1 1717556
#> ---
#> 2712: 1111111122 1111111183 0.05572782 1 1111111122
#> 2713: 1111111134 1111111183 0.04256283 1 1111111134
#> 2714: 1111111146 1111111183 0.05212860 1 1111111146
#> 2715: 1111111161 1111111183 0.04050542 2 1111111161
#> 2716: 1111111182 1111111183 0.27060404 8 1111111182
#> Target
#> <int>
#> 1: 1184127
#> 2: 2207578
#> 3: 2901822
#> 4: 2901822
#> 5: 2901822
#> ---
#> 2712: 1111111183
#> 2713: 1111111183
#> 2714: 1111111183
#> 2715: 1111111183
#> 2716: 1111111183The output is an edge list:
-
fromandtoare the identifiers of the two documents (as characters, which is what graph packages such astidygraphexpect; setoutput_in_character = FALSEto skip them); -
weightis the weight of the tie; -
nb_shared_referencesis the number of references the two documents share. It is displayed only ifnormalized_weight_only = FALSE; -
SourceandTargetkeep the original identifiers (with their original type). Each pair appears once, withSource < Target: the network is undirected.
The default weight: the coupling angle
By default, the weight is the coupling angle (or cosine) of Sen and Gan (1983), the standard way of normalising coupling. It divides the number of references two documents share by the geometric mean of the lengths of their bibliographies:
w_{AB} = \frac{|R(A) \cap R(B)|}{\sqrt{L(A) \, L(B)}}
where R(A) is the set of references of document A, |R(A) \cap R(B)| the number of references shared by A and B, and L(A) = |R(A)| the length of the bibliography of A. Without the denominator, a literature review with 200 references would be linked to almost everybody, simply because it cites a lot. The weight lies between 0 (nothing in common) and 1 (identical bibliographies). The same measure is available under its own name, coupling_angle(), which is what biblio_coupling() calls when you do not choose another method.
What counts as the length of a bibliography?
L(A) counts all the references of A present in your table, including those that no other document cites. They cannot create a tie, but they make the bibliography longer, and so they lower the weights of A. If you want to ignore them, remove them from the table before calling the function.
Choosing the minimal number of shared references
In a large corpus, sharing a single reference is weak evidence that two documents are related, and keeping all such pairs produces very dense networks. weight_threshold sets the minimal number of shared references for a pair to be kept. It applies to the number of shared references, not to the normalised weight.
biblio_coupling(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
weight_threshold = 3)#> 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
#> ---
#> 958: 39858452 1111111180 0.06596992 39858452 1111111180
#> 959: 151268764 1111111180 0.09464970 151268764 1111111180
#> 960: 1021902 1111111183 0.08674724 1021902 1111111183
#> 961: 106566092 1111111183 0.05710402 106566092 1111111183
#> 962: 1111111182 1111111183 0.27060404 1111111182 1111111183Raising the threshold is also the simplest way to keep a network tractable.
Very popular references and memory
The functions first list the pairs of documents that cite a same reference. A reference cited by n documents creates n(n-1)/2 pairs: a classic cited by 50,000 documents creates more than a billion of them. The package uses sparse matrices to keep this under control, but very popular references can still exhaust the memory of your computer on a large corpus. Split the corpus (by time window, for instance) or remove the most cited references before building the network.
Other weights: the method argument
The coupling angle gives the same importance to every shared reference. But two documents that both cite a classic cited by half of the corpus are not as clearly related as two documents that both cite an obscure article. Several measures take this into account, in the spirit of the tf-idf weighting of information retrieval (Spärck Jones 1972). They are all available through the method argument of biblio_coupling(), and each has its own function:
method |
Function | Intuition |
|---|---|---|
"angle" (default) |
coupling_angle() |
Shared references relative to the length of the two bibliographies (a cosine) (Sen and Gan 1983). |
"jaccard" |
coupling_jaccard() |
Of everything the two documents cite, the share they both cite (Sen and Gan 1983). |
"strength" |
coupling_strength() |
A shared rare reference counts more than a shared classic (Vladutz and Cook 1984; Shen et al. 2019). |
"similarity" |
coupling_similarity() |
The same idea, as a cosine bounded by 1 (Shen et al. 2019). |
"vladutz" |
coupling_vladutz() |
A shared reference counts 1/f_j: a very steep discount of popular references (Vladutz and Cook 1984). |
In the formulas below, N is the number of citing documents in the table and f_j the number of documents that cite the reference j (its frequency): the weight \log(N/f_j) of a reference is the inverse document frequency (idf), high for rare references and close to zero for references cited by almost everybody.
Coupling strength (Shen et al. 2019) sums the idf of the shared references, and divides by the lengths of the two bibliographies:
w_{AB} = \frac{1}{L(A) \, L(B)} \sum_{j \in R(A) \cap R(B)} \log\left(\frac{N}{f_j}\right)
Use it when a few references are cited by most documents of your corpus (the classics of the field): sharing them says little about the proximity of two documents. The price is a measure that depends on the whole corpus, and whose scale (it is not bounded by 1) is not comparable across corpora.
biblio_coupling(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
method = "strength",
weight_threshold = 3)#> from to weight Source Target
#> <char> <char> <num> <int> <int>
#> 1: 214927 2207578 0.020008623 214927 2207578
#> 2: 5160307 6714008 0.010611749 5160307 6714008
#> 3: 1717556 7815498 0.035262345 1717556 7815498
#> 4: 214927 8456979 0.011939901 214927 8456979
#> 5: 2207578 8456979 0.012807897 2207578 8456979
#> ---
#> 958: 39858452 1111111180 0.005118578 39858452 1111111180
#> 959: 151268764 1111111180 0.007465000 151268764 1111111180
#> 960: 1021902 1111111183 0.006925280 1021902 1111111183
#> 961: 106566092 1111111183 0.002896722 106566092 1111111183
#> 962: 1111111182 1111111183 0.038292193 1111111182 1111111183Coupling similarity (Shen et al. 2019, Eq. 8) is the idf-weighted cosine. Each document is described by the “informational size” of its bibliography, S(A) = \sum_{j \in R(A)} \log(N/f_j), and
w_{AB} = \frac{\sum_{j \in R(A) \cap R(B)} \log(N/f_j)}{\sqrt{S(A) \, S(B)}}
It generalises the coupling angle (if all the references had the same idf, we would get the angle back) and is bounded by 1.
coupling_similarity(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
weight_threshold = 3)#> from to weight Source Target
#> <char> <char> <num> <int> <int>
#> 1: 214927 2207578 0.12438825 214927 2207578
#> 2: 5160307 6714008 0.07382317 5160307 6714008
#> 3: 1717556 7815498 0.13924311 1717556 7815498
#> 4: 214927 8456979 0.08470689 214927 8456979
#> 5: 2207578 8456979 0.09897134 2207578 8456979
#> ---
#> 958: 39858452 1111111180 0.05799043 39858452 1111111180
#> 959: 151268764 1111111180 0.07948371 151268764 1111111180
#> 960: 1021902 1111111183 0.05330234 1021902 1111111183
#> 961: 106566092 1111111183 0.03780964 106566092 1111111183
#> 962: 1111111182 1111111183 0.24285542 1111111182 1111111183The two other measures are mostly useful for comparison. coupling_jaccard() divides the number of shared references by the size of the union of the two bibliographies, and penalises more strongly pairs of bibliographies of very different lengths. coupling_vladutz() implements the first formula that discounted popular references (Vladutz and Cook 1984), which Shen et al. (2019) later corrected with the idf.
Comparing the measures on your corpus
The measures do not have the same scale, so their weights cannot be compared directly, but their distributions and rankings can. compute_couplings() computes several measures at once (listing the pairs of documents only once), and summarise_weights(), correlate_weights(), overlap_top_weights(), merge_weights() and plot_weights() compare them.
measures <- compute_couplings(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
weight_threshold = 2)
# Rank correlation between the measures (1 = the same ranking of the pairs)
round(correlate_weights(measures), 2)#> angle strength similarity jaccard vladutz
#> angle 1.00 0.85 0.96 0.98 0.69
#> strength 0.85 1.00 0.90 0.81 0.73
#> similarity 0.96 0.90 1.00 0.94 0.84
#> jaccard 0.98 0.81 0.94 1.00 0.70
#> vladutz 0.69 0.73 0.84 0.70 1.00
#> attr(,"n_pairs")
#> [1] 1501Whether the choice of the measure matters on your corpus, which pairs of documents the measures disagree on, and how the communities change is the subject of the vignette on comparing measures.
Co-citation: biblio_cocitation()
Coupling links the documents that cite; co-citation links the documents that are cited: two references are co-cited when a same document cites both (Small 1973). It is the mirror image of coupling, and it is obtained by swapping the roles of the two columns. biblio_cocitation() does the swap for you: the citing documents stay in source and the references in ref, and the nodes of the network are the references.
biblio_cocitation(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
weight_threshold = 2)#> from to weight Source Target
#> <char> <char> <num> <int> <int>
#> 1: 181882 214939 0.2121320 181882 214939
#> 2: 214931 214939 0.2581989 214931 214939
#> 3: 181882 364710 0.3162278 181882 364710
#> 4: 214939 364710 0.2236068 214939 364710
#> 5: 181483 364716 0.6123724 181483 364716
#> ---
#> 4495: 51129176 1111112159 1.0000000 51129176 1111112159
#> 4496: 1111111579 1111112159 1.0000000 1111111579 1111112159
#> 4497: 1111111590 1111112159 1.0000000 1111111590 1111112159
#> 4498: 1111111595 1111112159 1.0000000 1111111595 1111112159
#> 4499: 1111111802 1111112159 1.0000000 1111111802 1111112159You get the same result by hand with biblio_coupling(), by inverting the two columns:
by_hand <- biblio_coupling(Ref_stagflation,
source = "ItemID_Ref",
ref = "Citing_ItemID_Ref",
weight_threshold = 2)
all.equal(by_hand, biblio_cocitation(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
weight_threshold = 2))#> [1] TRUEbiblio_cocitation() also has a method argument, with the same measures as coupling. There is a difference of interpretation, though: coupling ties are fixed once the documents are published (they depend only on their own bibliographies), whereas co-citation ties change as new documents cite the references. Coupling is therefore better suited to comparing successive time windows, and co-citation to describing how a literature is perceived at a given moment.
Aggregating at the level of entities: entity_network()
You may want to link authors, institutions or journals rather than documents. This is not a different kind of network, nor a different measure: it is the same coupling (or co-citation), computed for entities that aggregate documents. An entity publishes several documents and can cite the same reference several times. entity_network() takes this into account: for each reference shared by two entities, it counts the minimum number of times the two entities cite it (Zhao and Strotmann 2008). If one author cites a reference in two of their articles and another in three, the reference counts for two.
The consequence is that a reference that two entities cite repeatedly contributes more to the tie than a reference each of them cites once. With the coupling strength, the weight is
w_{AB} = \frac{1}{L(A) \, L(B)} \sum_{j} \min(C_{Aj}, C_{Bj}) \, \log\left(\frac{N}{f_j}\right)
where C_{Aj} and C_{Bj} are the numbers of times A and B cite the reference j, L(A) is the total number of citations made by A, N the number of citing documents and f_j the number of documents citing j. The method argument accepts the same methods as biblio_coupling() ("angle", "strength", "similarity", "jaccard" and "vladutz"), each adapted with the minimum rule (see ?entity_network for the formulas), and the network argument chooses between "coupling" (entities that cite the same references) and "cocitation" (entities whose references are cited together, as in author co-citation analysis).
The input needs one row per citation and per entity: we merge the table of direct citations with the table of authors. A document with several authors appears several times, hence allow.cartesian = TRUE.
entity_citations <- merge(Ref_stagflation,
Authors_stagflation,
by.x = "Citing_ItemID_Ref",
by.y = "ItemID_Ref",
allow.cartesian = TRUE)
entity_network(entity_citations,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
entity = "Author.y",
method = "angle")#> from to weight Source Target Weighting_method
#> <char> <char> <num> <char> <char> <char>
#> 1: ALBANESI-S BALL-L 0.048592953 ALBANESI-S BALL-L angle
#> 2: ALBANESI-S BARSKY-R 0.063021872 ALBANESI-S BARSKY-R angle
#> 3: ALBANESI-S BEYER-A 0.034585723 ALBANESI-S BEYER-A angle
#> 4: ALBANESI-S BILBIIE-FO 0.064282435 ALBANESI-S BILBIIE-FO angle
#> 5: ALBANESI-S BORDO-M 0.043519414 ALBANESI-S BORDO-M angle
#> ---
#> 3461: WILLIAMS-J WILLIAMS-N 0.028213825 WILLIAMS-J WILLIAMS-N angle
#> 3462: WILLIAMS-J YOUNG-W 0.008748736 WILLIAMS-J YOUNG-W angle
#> 3463: WILLIAMS-J ZHA-T 0.028213825 WILLIAMS-J ZHA-T angle
#> 3464: WILLIAMS-N ZHA-T 1.000000000 WILLIAMS-N ZHA-T angle
#> 3465: WOODFORD-M YOUNG-W 0.020672456 WOODFORD-M YOUNG-W angleFor a co-citation network of entities, the entity column must describe the cited reference (the author or the journal of the cited document) rather than the citing one. Here, the journals of the cited documents:
entity_network(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
entity = "Journal",
network = "cocitation",
weight_threshold = 3)#> Warning: Dropping 738 rows with a missing identifier.#> from to weight Source
#> <char> <char> <num> <char>
#> 1: 15 EUR CENTR BANK AM ECON REV 0.1513300 15 EUR CENTR BANK
#> 2: 15 EUR CENTR BANK CARNEGIE-ROCHESTER C 0.2773501 15 EUR CENTR BANK
#> 3: 15 EUR CENTR BANK ECON INQ 0.6546537 15 EUR CENTR BANK
#> 4: 15 EUR CENTR BANK J MONETARY ECON 0.1568125 15 EUR CENTR BANK
#> 5: 15 EUR CENTR BANK MONETARY POLICY RULE 0.2672612 15 EUR CENTR BANK
#> ---
#> 1010: REV ECON DYNAM REV ECON STAT 0.2433321 REV ECON DYNAM
#> 1011: REV ECON DYNAM REV ECON STUD 0.3746343 REV ECON DYNAM
#> 1012: REV ECON STAT REV ECON STUD 0.2525907 REV ECON STAT
#> 1013: REV ECON STUD STUDIES BUSINESS CYC 0.3535534 REV ECON STUD
#> 1014: REV ECON STUD UNPUB WHY INFLATION 0.3535534 REV ECON STUD
#> Target Weighting_method
#> <char> <char>
#> 1: AM ECON REV angle
#> 2: CARNEGIE-ROCHESTER C angle
#> 3: ECON INQ angle
#> 4: J MONETARY ECON angle
#> 5: MONETARY POLICY RULE angle
#> ---
#> 1010: REV ECON STAT angle
#> 1011: REV ECON STUD angle
#> 1012: REV ECON STUD angle
#> 1013: STUDIES BUSINESS CYC angle
#> 1014: UNPUB WHY INFLATION angleCo-authorship: coauth_network()
Co-authorship links the authors (or institutions, or countries) who sign documents together. You could build it with biblio_coupling(), authors being the source and documents the ref, but coupling is not designed for it: what matters here is how to count a collaboration. coauth_network() offers three ways, and an optional normalisation by the productivity of the authors.
To see what they do, take a toy example: three authors, a, b and c, sign document 1; a and b sign document 2.
toy <- data.frame(author = c("a", "b", "c", "a", "b"),
paper = c(1, 1, 1, 2, 2))Full counting ("full_counting") gives one point to each pair of authors for each document they co-sign. The weight is the number of co-signed documents. Here a–b gets 2 points, and a–c and b–c one point each. The problem is that big collaborations weigh more: a document with ten authors creates 45 pairs, so it adds 45 points to the network, whereas a document with two authors adds one.
coauth_network(toy, authors = "author", articles = "paper", method = "full_counting")#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: b a 2 b a
#> 2: c a 1 c a
#> 3: c b 1 c bFractional counting ("fractional_counting") shares the value of a document among the co-authors, so that a large collaboration does not dominate (Perianes-Rodriguez, Waltman, and Van Eck 2016). A document with n authors gives 1/(n-1) to each pair of its authors, so that the weights of all the ties of an author in this document sum to one: each author “spends” one unit of collaboration per document, split among the co-authors. In the toy example, document 1 has three authors, so each of its three pairs receives 1/2; document 2 has two authors, so a–b receives 1. The weight of a–b is 1/2 + 1 = 1.5, and that of a–c and b–c is 1/2: the pair that collaborated in a small team is worth more than a pair in a large team. Perianes-Rodriguez, Waltman, and Van Eck (2016) compare full and fractional counting on bibliometric networks, and show that the choice changes the picture.
coauth_network(toy, authors = "author", articles = "paper", method = "fractional_counting")#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: b a 1.5 b a
#> 2: c a 0.5 c a
#> 3: c b 0.5 c bRefined fractional counting ("fractional_counting_refined"), inspired by Leydesdorff and Park (2017-02), goes one step further: each document, rather than each author, has a total weight of one in the network. A document with n authors creates n(n-1)/2 pairs, so each pair gets 2/(n(n-1)). Document 1 gives 1/3 to each of its three pairs (3 \times 1/3 = 1) and document 2 gives 1 to a–b. The weight of a–b is 1/3 + 1 \approx 1.33. The sum of all the weights of the network is then the number of co-authored documents.
coauth_network(toy, authors = "author", articles = "paper", method = "fractional_counting_refined")#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: b a 1.3333333 b a
#> 2: c a 0.3333333 c a
#> 3: c b 0.3333333 c bIn all cases, documents with a single author are ignored, since they create no tie.
Normalising by productivity. Prolific authors have many collaborations simply because they publish a lot. With cosine_normalized = TRUE, the weight is divided by \sqrt{P_i P_j}, where P_i is the number of co-authored documents of author i (Salton’s cosine, as for the coupling angle). The weight then measures whether two authors collaborate a lot relative to how much each of them collaborates in general. In the toy example, P_a = P_b = 2 and P_c = 1: with full counting, a–b gets 2/\sqrt{2 \times 2} = 1 and a–c gets 1/\sqrt{2 \times 1} \approx 0.71.
coauth_network(toy, authors = "author", articles = "paper",
method = "full_counting", cosine_normalized = TRUE)#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: b a 1.0000000 b a
#> 2: c a 0.7071068 c a
#> 3: c b 0.7071068 c bOn the stagflation authors, with fractional counting and the cosine normalisation:
coauth_network(Authors_stagflation,
authors = "Author",
articles = "ItemID_Ref",
method = "fractional_counting",
cosine_normalized = TRUE)#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: CHARI-V ALBANESI-S 0.3535534 CHARI-V ALBANESI-S
#> 2: CHRISTIANO-L ALBANESI-S 0.2500000 CHRISTIANO-L ALBANESI-S
#> 3: CHRISTIANO-L CHARI-V 0.3535534 CHRISTIANO-L CHARI-V
#> 4: CUKIERMAN-A BRUNNER-K 0.3535534 CUKIERMAN-A BRUNNER-K
#> 5: EICHENBAUM-M CHARI-V 0.3535534 EICHENBAUM-M CHARI-V
#> 6: EICHENBAUM-M CHRISTIANO-L 0.2500000 EICHENBAUM-M CHRISTIANO-L
#> 7: EICHENGREEN-B BORDO-M 1.0000000 EICHENGREEN-B BORDO-M
#> 8: EUSEPI-S BULLARD-J 1.0000000 EUSEPI-S BULLARD-J
#> 9: FARMER-R BEYER-A 1.0000000 FARMER-R BEYER-A
#> 10: FITZGERALD-T CHRISTIANO-L 0.5000000 FITZGERALD-T CHRISTIANO-L
#> 11: GALI-J BLANCHARD-O 0.7071068 GALI-J BLANCHARD-O
#> 12: GALI-J CLARIDA-R 0.3535534 GALI-J CLARIDA-R
#> 13: GERTLER-M BERNANKE-B 0.3535534 GERTLER-M BERNANKE-B
#> 14: GERTLER-M CLARIDA-R 0.3535534 GERTLER-M CLARIDA-R
#> 15: GERTLER-M GALI-J 0.2500000 GERTLER-M GALI-J
#> 16: GOODWIN-T GISSER-M 1.0000000 GOODWIN-T GISSER-M
#> 17: GORDON-R FRYE-J 1.0000000 GORDON-R FRYE-J
#> 18: GUST-C CHRISTIANO-L 0.5000000 GUST-C CHRISTIANO-L
#> 19: HALTIWANGER-J DAVIS-S 1.0000000 HALTIWANGER-J DAVIS-S
#> 20: HOOPER-P CECCHETTI-S 0.2500000 HOOPER-P CECCHETTI-S
#> 21: JACKMAN-R GRUBB-D 0.5000000 JACKMAN-R GRUBB-D
#> 22: KASMAN-B CECCHETTI-S 0.2500000 KASMAN-B CECCHETTI-S
#> 23: KASMAN-B HOOPER-P 0.2500000 KASMAN-B HOOPER-P
#> 24: KILIAN-L BARSKY-R 1.0000000 KILIAN-L BARSKY-R
#> 25: KING-R GOODFRIEND-M 1.0000000 KING-R GOODFRIEND-M
#> 26: LAYARD-R GRUBB-D 0.5000000 LAYARD-R GRUBB-D
#> 27: LAYARD-R JACKMAN-R 0.5000000 LAYARD-R JACKMAN-R
#> 28: LIPPI-F CUKIERMAN-A 0.7071068 LIPPI-F CUKIERMAN-A
#> 29: MANKIW-G BALL-L 1.0000000 MANKIW-G BALL-L
#> 30: MCGREGOR-R CHAPPELL-H 1.0000000 MCGREGOR-R CHAPPELL-H
#> 31: MELTZER-A BRUNNER-K 0.5000000 MELTZER-A BRUNNER-K
#> 32: MELTZER-A CUKIERMAN-A 0.3535534 MELTZER-A CUKIERMAN-A
#> 33: MORK-K HALL-R 1.0000000 MORK-K HALL-R
#> 34: NELSON-E DICECIO-C 1.0000000 NELSON-E DICECIO-C
#> 35: PAPELL-D NIKOLSKO-R 1.0000000 PAPELL-D NIKOLSKO-R
#> 36: PESAVENTO-E HERRERA-A 1.0000000 PESAVENTO-E HERRERA-A
#> 37: RASCHE-R POOLE-W 0.3535534 RASCHE-R POOLE-W
#> 38: ROMER-D ROMER-C 1.0000000 ROMER-D ROMER-C
#> 39: RUDD-J BLINDER-A 1.0000000 RUDD-J BLINDER-A
#> 40: SACHS-J BRUNO-M 1.0000000 SACHS-J BRUNO-M
#> 41: SARGENT-T COGLEY-T 0.8660254 SARGENT-T COGLEY-T
#> 42: SCHOENHOLTZ-K CECCHETTI-S 0.2500000 SCHOENHOLTZ-K CECCHETTI-S
#> 43: SCHOENHOLTZ-K HOOPER-P 0.2500000 SCHOENHOLTZ-K HOOPER-P
#> 44: SCHOENHOLTZ-K KASMAN-B 0.2500000 SCHOENHOLTZ-K KASMAN-B
#> 45: SILL-K LEDUC-S 0.5000000 SILL-K LEDUC-S
#> 46: STARK-T LEDUC-S 0.5000000 STARK-T LEDUC-S
#> 47: STARK-T SILL-K 0.5000000 STARK-T SILL-K
#> 48: STRAUB-R BILBIIE-FO 1.0000000 STRAUB-R BILBIIE-FO
#> 49: TATOM-J RASCHE-R 0.7071068 TATOM-J RASCHE-R
#> 50: TAYLOR-J LEVIN-A 1.0000000 TAYLOR-J LEVIN-A
#> 51: TINSLEY-P KOZICKI-S 1.0000000 TINSLEY-P KOZICKI-S
#> 52: WATSON-M BERNANKE-B 0.3535534 WATSON-M BERNANKE-B
#> 53: WATSON-M CECCHETTI-S 0.1767767 WATSON-M CECCHETTI-S
#> 54: WATSON-M GERTLER-M 0.2500000 WATSON-M GERTLER-M
#> 55: WATSON-M HOOPER-P 0.1767767 WATSON-M HOOPER-P
#> 56: WATSON-M KASMAN-B 0.1767767 WATSON-M KASMAN-B
#> 57: WATSON-M SCHOENHOLTZ-K 0.1767767 WATSON-M SCHOENHOLTZ-K
#> 58: WHEELOCK-D POOLE-W 0.5000000 WHEELOCK-D POOLE-W
#> 59: WHEELOCK-D RASCHE-R 0.3535534 WHEELOCK-D RASCHE-R
#> 60: WILLIAMS-J ORPHANIDES-A 1.0000000 WILLIAMS-J ORPHANIDES-A
#> 61: WILLIAMS-N SARGENT-T 0.2500000 WILLIAMS-N SARGENT-T
#> 62: WOODFORD-M ROTEMBERG-J 1.0000000 WOODFORD-M ROTEMBERG-J
#> 63: ZHA-T SARGENT-T 0.2500000 ZHA-T SARGENT-T
#> 64: ZHA-T WILLIAMS-N 0.5000000 ZHA-T WILLIAMS-N
#> from to weight Source Target
#> <char> <char> <num> <char> <char>Note that, for historical reasons, coauth_network() orients its edges with Source > Target, the opposite of the other functions.
Filtering the edges: thresholds and backbones
A bibliometric network built from a large corpus is often too dense to be read or clustered: almost every pair of documents shares at least one reference. There are two ways of simplifying it.
-
A threshold, as seen above:
weight_thresholdkeeps the pairs sharing at least k references. It is simple and fast, but arbitrary, and it is global: the same threshold applies to a document with a hundred references and to a document with five. -
A backbone: keep only the ties that are statistically unlikely under a null model, that is, the ties that are stronger than what the position of the nodes in the network would produce by chance. This is the aim of the
backbonepackage (Neal 2026), which is complementary tobiblionetwork:biblionetworkcomputes the edges and their weights,backbonedecides which ones are worth keeping.
backbone offers two families of methods, and they do not start from the same object.
Filters of weighted networks (backbone_from_weighted(), with the disparity filter of Serrano, Boguñá, and Vespignani (2009) for instance) start from a weighted one-mode network. They can be run directly on the edges produced by biblionetwork: convert the edge list into a graph and give it to backbone. Since these filters assume that the weights are strengths of ties, it is more natural to feed them with the number of shared references (normalized_weight_only = FALSE) than with a cosine.
edges <- biblio_coupling(Ref_stagflation,
source = "Citing_ItemID_Ref",
ref = "ItemID_Ref",
normalized_weight_only = FALSE,
weight_threshold = 2)
# The weighted graph; the number of shared references is the weight
graph <- igraph::graph_from_data_frame(
edges[, .(from, to, weight = nb_shared_references)],
directed = FALSE
)
# The disparity filter: keep an edge if its weight is significantly high
# compared to the other edges of (at least one of) its two nodes
backbone <- backbone::backbone_from_weighted(graph, model = "disparity", alpha = 0.05)
c(edges_before = igraph::ecount(graph), edges_after = igraph::ecount(backbone))#> edges_before edges_after
#> 1501 16Filters of bipartite projections (backbone_from_projection(), with models such as "sdsm", the stochastic degree sequence model) do not start from the edges but from the original two-mode table: they compare the number of references that two documents share with the number expected if documents cited references at random, given how many references each document cites and how many documents cite each reference. The input is the table of citations as an incidence matrix (documents in rows, references in columns), which is the same table as the one you give to biblionetwork.
# Incidence matrix of the citations: 1 if the document (row) cites the reference (column)
incidence <- unclass(table(Ref_stagflation$Citing_ItemID_Ref, Ref_stagflation$ItemID_Ref))
incidence[incidence > 1] <- 1
# Statistically significant coupling ties (the filter is applied to the rows)
backbone_sdsm <- backbone::backbone_from_projection(incidence, model = "sdsm", alpha = 0.05)
sum(backbone_sdsm) / 2 # number of ties kept (the matrix is symmetric)#> [1] 553Two practical remarks.
- The statistical models test the count of shared references, not a normalised weight. Run them on the full table, without a
weight_threshold: a pair removed by the threshold cannot be tested. The backbone then replaces the threshold. You can usebiblionetworkafterwards, on the pairs kept, if you want the normalised weights of the surviving ties (merge the two edge lists by pair of documents). - These tests are computationally heavier than the edge computation of
biblionetwork, and the null models are not designed for the huge corpora thatbiblionetworkhandles: on a large corpus, split it by time window, or start from the filters of weighted networks.
networkflow integrates both steps: its function build_dynamic_networks() can compute the coupling edges and apply a statistical backbone for each time window (see the networkflow documentation).
Beyond bibliometrics
Nothing in the functions of biblionetwork is specific to bibliography. They take a table with two columns, “a source that is linked to a ref”, and build the network of the sources that share refs (coupling) or of the refs that share sources (co-citation). The words “document” and “reference” are only the vocabulary of the field in which the package was written. Whenever you have a two-mode relation, the same questions can be asked:
| Source (“citing”) | Ref (“cited”) | Coupling links sources that… | Co-citation links refs that… |
|---|---|---|---|
| article | reference | cite the same references | are cited by the same articles |
| social media account | account followed | follow the same accounts (an audience in common) | are followed by the same accounts |
| social media account | post reposted | repost the same posts | are reposted by the same accounts |
| post | hashtag, link, mention | use the same hashtags, links or mentions | are used in the same posts |
| document | word | use the same words | appear in the same documents |
Networks of accounts on a social media platform
Take a table of the accounts of a social media platform and the accounts they follow. Two accounts that follow many of the same accounts probably listen to the same voices: this is the bibliographic coupling of the “follows” (the account is the “document”, the accounts it follows are its “bibliography”). In the same way, two accounts that repost the same posts are close in what they amplify. The following table is invented, for the sake of the example.
follows <- data.table(
account = c("ann", "ann", "ann", "ben", "ben", "ben", "cleo", "cleo", "dan", "dan", "eve", "eve", "eve"),
follows = c("news_desk", "dev_tools", "open_web", "news_desk", "dev_tools", "open_web",
"news_desk", "celebrity", "celebrity", "news_desk", "celebrity", "dev_tools", "open_web")
)
# Accounts close because they follow the same accounts
biblio_coupling(follows, source = "account", ref = "follows", normalized_weight_only = FALSE)#> from to weight nb_shared_references Source Target
#> <char> <char> <num> <int> <char> <char>
#> 1: ann ben 1.0000000 3 ann ben
#> 2: ann cleo 0.4082483 1 ann cleo
#> 3: ben cleo 0.4082483 1 ben cleo
#> 4: ann dan 0.4082483 1 ann dan
#> 5: ben dan 0.4082483 1 ben dan
#> 6: cleo dan 1.0000000 2 cleo dan
#> 7: ann eve 0.6666667 2 ann eve
#> 8: ben eve 0.6666667 2 ben eve
#> 9: cleo eve 0.4082483 1 cleo eve
#> 10: dan eve 0.4082483 1 dan eveHere news_desk and celebrity are followed by almost everybody: following them says little. The idf-based methods, designed for the “classics” of a bibliography, are exactly what is needed to discount the accounts followed by a large audience:
biblio_coupling(follows, source = "account", ref = "follows", method = "strength")#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: ann ben 0.13831053 ann ben
#> 2: ann cleo 0.03719059 ann cleo
#> 3: ben cleo 0.03719059 ben cleo
#> 4: ann dan 0.03719059 ann dan
#> 5: ben dan 0.03719059 ben dan
#> 6: cleo dan 0.18349229 cleo dan
#> 7: ann eve 0.11351681 ann eve
#> 8: ben eve 0.11351681 ben eve
#> 9: cleo eve 0.08513760 cleo eve
#> 10: dan eve 0.08513760 dan eveThis is how coupling is used on social media data: popular targets (an account followed by millions) are the equivalent of the classics of a field, and the warning on memory of Section 2 matters even more, as such targets are much more frequent than in a bibliography. Reposts work the same way, with source the account and ref the reposted post. And co-citation answers the mirror question: which posts are reposted by the same accounts?
reposts <- data.table(
account = c("ann", "ann", "ben", "ben", "cleo", "cleo", "dan"),
post = c("p1", "p2", "p1", "p2", "p2", "p3", "p3")
)
biblio_cocitation(reposts, source = "account", ref = "post")#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: p1 p2 0.8164966 p1 p2
#> 2: p2 p3 0.4082483 p2 p3Because a network of this kind is often dense (and the measures do not tell which ties are “surprising”), the backbone of Section 6 is particularly useful there.
Networks of words
A text is a “document” that “cites” words. The coupling of texts links the texts that use the same words; the co-citation of words links the words that appear together. We illustrate it with the titles of the stagflation documents.
titles <- Nodes_stagflation[!is.na(Title), .(ItemID_Ref, Title)]
# One row per title and distinct word. Short words and a few stop words are dropped:
# like popular references, very frequent words create a huge number of pairs and carry little meaning.
stop_words <- c("the", "and", "for", "with", "from", "that", "this", "its", "are", "was",
"into", "their", "between", "some", "what", "how", "when", "than", "have", "new")
words <- titles[, .(word = unique(tolower(unlist(strsplit(Title, "[^A-Za-z]+"))))), by = ItemID_Ref]
words <- words[nchar(word) > 3 & !word %in% stop_words]
words[1:5]#> ItemID_Ref word
#> <char> <char>
#> 1: 112854189 richard
#> 2: 112854189 nixon
#> 3: 112854189 pressured
#> 4: 112854189 arthur
#> 5: 112854189 burnsTitles are coupled when they share words. The coupling strength gives more weight to rare words than to words such as “inflation” or “policy”, present in many titles:
title_edges <- biblio_coupling(words, source = "ItemID_Ref", ref = "word",
method = "strength", normalized_weight_only = FALSE,
weight_threshold = 2)
title_edges[order(-weight)][1:5]#> from to weight nb_shared_references Source Target
#> <char> <char> <num> <int> <char> <char>
#> 1: 15862899 804985 2.172583 2 15862899 804985
#> 2: 105203318 927924 1.563913 2 105203318 927924
#> 3: 1111111190 49791437 1.376890 2 1111111190 49791437
#> 4: 37660505 6071710 1.376890 2 37660505 6071710
#> 5: 37799073 44208484 1.350867 3 37799073 44208484Words are linked when they appear in the same titles (this is the co-citation of words). The words that always appear together are the fixed expressions of the corpus:
word_edges <- biblio_cocitation(words, source = "ItemID_Ref", ref = "word",
weight_threshold = 2, normalized_weight_only = FALSE)
word_edges[order(-nb_shared_citations)][1:8, .(from, to, weight, nb_shared_citations)]#> from to weight nb_shared_citations
#> <char> <char> <num> <int>
#> 1: monetary policy 0.7441311 97
#> 2: great inflation 0.3400046 23
#> 3: inflation policy 0.1533110 22
#> 4: states united 0.9770084 21
#> 5: policy rules 0.3127716 18
#> 6: inflation monetary 0.1154735 15
#> 7: monetary rules 0.2687343 14
#> 8: price shocks 0.3614784 14The same logic applies to any “bag of …” representation (n-grams, keywords, hashtags, named entities, topics of a topic model…). For the words in the titles of references, coupling_descriptive() implements a more elaborate approach (Liu 2017), which couples documents that cite different but related references.
What to check before using it outside bibliometrics
-
Orientation.
sourceis the node of the network produced bybiblio_coupling();refis what the nodes share. If the network you obtain has the wrong nodes, you probably swapped the columns (the function warns you when no pair is found). - Popular targets. A target shared by very many sources (a celebrity, a stop word) creates a quadratic number of pairs and carries little information. Remove it, or use a method that discounts it, or work by time window.
- The meaning of “length”. The normalisation by the length of the bibliography assumes that having many refs is a form of dilution. For an account following 10,000 accounts, this is reasonable; for a text, the length of the document in words may be a different matter.
- Time. Coupling ties are fixed when the source is created. For social media data, the “follows” are not dated in the same way as references: think about the moment at which the table is observed.
A last word on choosing
| Question | Nodes | Function |
|---|---|---|
| Which documents rely on the same literature? Which research fronts? (Kessler 1963; Boyack and Klavans 2010) | citing documents | biblio_coupling() |
| Same, but not driven by the classics of the corpus (Shen et al. 2019) | citing documents |
biblio_coupling(method = "strength") or "similarity"
|
| Does the choice of the measure matter on my corpus? | citing documents |
compute_couplings(), then correlate_weights(), plot_weights()
|
| Which authors, journals or institutions rely on the same literature (or are cited together)? (Zhao and Strotmann 2008) | entities | entity_network() |
| Which cited texts are perceived as belonging together? (Small 1973) | cited references | biblio_cocitation() |
| Who collaborates with whom? (Perianes-Rodriguez, Waltman, and Van Eck 2016; Leydesdorff and Park 2017-02) | authors, institutions, countries | coauth_network() |
| Which of these ties are not due to chance? (Neal 2026) | any | the backbone package |
All the functions return undirected edges (one row per pair), never modify the table you give them, and return an empty table, with a warning that says why, when no pair of nodes is linked.