Builds the edges of a co-authorship network from a table with one row per author (or institution, or country) and document. Two authors are linked when they have co-signed documents. The weight of the tie can count each collaboration fully, or share it between the pairs of co-authors of a document (fractional counting), following (Perianes-Rodriguez et al. 2016; Leydesdorff and Park 2017-02) , and can be normalised by the productivity of the two authors with a cosine.
Usage
coauth_network(
dt,
authors,
articles,
method = c("full_counting", "fractional_counting", "fractional_counting_refined"),
cosine_normalized = FALSE
)Arguments
- dt
A data frame or a
data.tablewith one row per author and document. It is not modified.Character scalar. The column of the authors (or institutions, or countries), the nodes of the network.
- articles
Character scalar. The column of the documents.
- method
"full_counting"(default),"fractional_counting"or"fractional_counting_refined"(see the details).- cosine_normalized
Logical. If
TRUE, divides the weight by the geometric mean of the numbers of co-authored documents of the two authors (Salton's cosine).
Value
A data.table with one row per pair of authors: from and to
(copies of Source and Target, with the type of the authors
column), the weight, and the original identifiers in Source and
Target. Each pair appears once, with Source > Target (the orientation of
the previous versions of the package).
Details
![[Experimental]](figures/lifecycle-experimental.svg)
Write \(a_{ik} = 1\) if author \(i\) signed document \(k\), and
\(n_k = \sum_i a_{ik}\) for its number of authors. The weight of the tie
between \(i\) and \(j\) is, according to method:
"full_counting": the number of documents they co-signed, $$w_{ij} = \sum_{k} a_{ik} a_{jk}$$"fractional_counting"(Perianes-Rodriguez et al. 2016) : each document gives \(1/(n_k - 1)\) to each pair, $$w_{ij} = \sum_{k} \frac{a_{ik} a_{jk}}{n_k - 1}$$ so that the weights of the ties of an author in a document sum to 1;"fractional_counting_refined", inspired by (Leydesdorff and Park 2017-02) : each document gives \(2 / (n_k (n_k - 1))\) to each pair, $$w_{ij} = \sum_{k} \frac{2 \, a_{ik} a_{jk}}{n_k (n_k - 1)}$$ so that each document has a total weight of 1 in the network: the sum of all the weights equals the number of (multi-authored) documents.
If cosine_normalized = TRUE, the weight is divided by
\(\sqrt{P_i P_j}\), with \(P_i\) the number of co-authored documents
of author \(i\) (documents with a single author are ignored in the
whole function, since they create no tie).
Duplicated rows are counted once, rows with a missing identifier are dropped with a warning, the table of the user is not modified, and a zero-row table is returned, with a warning, if nobody co-authored a document.
Why use it in research
Co-authorship networks describe the social structure of a research community: who collaborates with whom, the existence of collaborative cliques, the central or bridging positions. The way collaborations are counted changes the picture. With full counting, a document signed by ten authors creates 45 ties of weight 1 and weighs much more in the network than a document signed by two authors; fractional counting corrects this by giving a document a total weight that does not depend on its number of authors. Normalising by productivity prevents very prolific authors from being linked to everybody. Perianes-Rodriguez et al. (Perianes-Rodriguez et al. 2016) compare full and fractional counting for bibliometric networks: read it before choosing. The nodes can be authors, institutions or countries, the latter being the basis of studies of international collaboration.
Intuition
Think of each document as a pie of value 1 to share among the pairs of its authors. With full counting, every pair of co-authors receives a full pie: a document with ten authors distributes 45 pies, a document with two authors distributes one. With fractional counting, a document always distributes the same total (one pie in the refined version, or one pie per author in the other), so that large collaborations do not dominate. The cosine then asks whether two authors collaborate much relative to how much each of them collaborates in general.
References
Leydesdorff L, Park HW (2017-02).
“Full and Fractional Counting in Bibliometric Networks.”
Journal of Informetrics, 11(1), 117–120.
ISSN 17511577.
https://linkinghub.elsevier.com/retrieve/pii/S1751157716303133.
Perianes-Rodriguez A, Waltman L, Van Eck NJ (2016).
“Constructing Bibliometric Networks: A Comparison between Full and Fractional Counting.”
Journal of Informetrics, 10(4), 1178–1195.
https://www.sciencedirect.com/science/article/pii/S1751157716302036?casa_token=AtzjmZ-1QmYAAAAA:2mlBPZsjGUleYi9mnybHODFw2RmMh3GHvRAuMYXygRm63cQOv07M4ixbAmJXuGq71tx2ug29baTp.
See also
Other co-citation and co-authorship measures:
biblio_cocitation()
Examples
library(biblionetwork)
coauth_network(Authors_stagflation,
authors = "Author",
articles = "ItemID_Ref",
method = "fractional_counting")
#> from to weight Source Target
#> <char> <char> <num> <char> <char>
#> 1: CHARI-V ALBANESI-S 0.50 CHARI-V ALBANESI-S
#> 2: CHRISTIANO-L ALBANESI-S 0.50 CHRISTIANO-L ALBANESI-S
#> 3: CHRISTIANO-L CHARI-V 1.00 CHRISTIANO-L CHARI-V
#> 4: CUKIERMAN-A BRUNNER-K 0.50 CUKIERMAN-A BRUNNER-K
#> 5: EICHENBAUM-M CHARI-V 0.50 EICHENBAUM-M CHARI-V
#> 6: EICHENBAUM-M CHRISTIANO-L 0.50 EICHENBAUM-M CHRISTIANO-L
#> 7: EICHENGREEN-B BORDO-M 1.00 EICHENGREEN-B BORDO-M
#> 8: EUSEPI-S BULLARD-J 1.00 EUSEPI-S BULLARD-J
#> 9: FARMER-R BEYER-A 1.00 FARMER-R BEYER-A
#> 10: FITZGERALD-T CHRISTIANO-L 1.00 FITZGERALD-T CHRISTIANO-L
#> 11: GALI-J BLANCHARD-O 1.00 GALI-J BLANCHARD-O
#> 12: GALI-J CLARIDA-R 0.50 GALI-J CLARIDA-R
#> 13: GERTLER-M BERNANKE-B 0.50 GERTLER-M BERNANKE-B
#> 14: GERTLER-M CLARIDA-R 0.50 GERTLER-M CLARIDA-R
#> 15: GERTLER-M GALI-J 0.50 GERTLER-M GALI-J
#> 16: GOODWIN-T GISSER-M 1.00 GOODWIN-T GISSER-M
#> 17: GORDON-R FRYE-J 2.00 GORDON-R FRYE-J
#> 18: GUST-C CHRISTIANO-L 1.00 GUST-C CHRISTIANO-L
#> 19: HALTIWANGER-J DAVIS-S 1.00 HALTIWANGER-J DAVIS-S
#> 20: HOOPER-P CECCHETTI-S 0.25 HOOPER-P CECCHETTI-S
#> 21: JACKMAN-R GRUBB-D 0.50 JACKMAN-R GRUBB-D
#> 22: KASMAN-B CECCHETTI-S 0.25 KASMAN-B CECCHETTI-S
#> 23: KASMAN-B HOOPER-P 0.25 KASMAN-B HOOPER-P
#> 24: KILIAN-L BARSKY-R 2.00 KILIAN-L BARSKY-R
#> 25: KING-R GOODFRIEND-M 1.00 KING-R GOODFRIEND-M
#> 26: LAYARD-R GRUBB-D 0.50 LAYARD-R GRUBB-D
#> 27: LAYARD-R JACKMAN-R 0.50 LAYARD-R JACKMAN-R
#> 28: LIPPI-F CUKIERMAN-A 1.00 LIPPI-F CUKIERMAN-A
#> 29: MANKIW-G BALL-L 1.00 MANKIW-G BALL-L
#> 30: MCGREGOR-R CHAPPELL-H 1.00 MCGREGOR-R CHAPPELL-H
#> 31: MELTZER-A BRUNNER-K 0.50 MELTZER-A BRUNNER-K
#> 32: MELTZER-A CUKIERMAN-A 0.50 MELTZER-A CUKIERMAN-A
#> 33: MORK-K HALL-R 2.00 MORK-K HALL-R
#> 34: NELSON-E DICECIO-C 1.00 NELSON-E DICECIO-C
#> 35: PAPELL-D NIKOLSKO-R 1.00 PAPELL-D NIKOLSKO-R
#> 36: PESAVENTO-E HERRERA-A 1.00 PESAVENTO-E HERRERA-A
#> 37: RASCHE-R POOLE-W 0.50 RASCHE-R POOLE-W
#> 38: ROMER-D ROMER-C 2.00 ROMER-D ROMER-C
#> 39: RUDD-J BLINDER-A 1.00 RUDD-J BLINDER-A
#> 40: SACHS-J BRUNO-M 3.00 SACHS-J BRUNO-M
#> 41: SARGENT-T COGLEY-T 3.00 SARGENT-T COGLEY-T
#> 42: SCHOENHOLTZ-K CECCHETTI-S 0.25 SCHOENHOLTZ-K CECCHETTI-S
#> 43: SCHOENHOLTZ-K HOOPER-P 0.25 SCHOENHOLTZ-K HOOPER-P
#> 44: SCHOENHOLTZ-K KASMAN-B 0.25 SCHOENHOLTZ-K KASMAN-B
#> 45: SILL-K LEDUC-S 0.50 SILL-K LEDUC-S
#> 46: STARK-T LEDUC-S 0.50 STARK-T LEDUC-S
#> 47: STARK-T SILL-K 0.50 STARK-T SILL-K
#> 48: STRAUB-R BILBIIE-FO 1.00 STRAUB-R BILBIIE-FO
#> 49: TATOM-J RASCHE-R 1.00 TATOM-J RASCHE-R
#> 50: TAYLOR-J LEVIN-A 1.00 TAYLOR-J LEVIN-A
#> 51: TINSLEY-P KOZICKI-S 1.00 TINSLEY-P KOZICKI-S
#> 52: WATSON-M BERNANKE-B 0.50 WATSON-M BERNANKE-B
#> 53: WATSON-M CECCHETTI-S 0.25 WATSON-M CECCHETTI-S
#> 54: WATSON-M GERTLER-M 0.50 WATSON-M GERTLER-M
#> 55: WATSON-M HOOPER-P 0.25 WATSON-M HOOPER-P
#> 56: WATSON-M KASMAN-B 0.25 WATSON-M KASMAN-B
#> 57: WATSON-M SCHOENHOLTZ-K 0.25 WATSON-M SCHOENHOLTZ-K
#> 58: WHEELOCK-D POOLE-W 0.50 WHEELOCK-D POOLE-W
#> 59: WHEELOCK-D RASCHE-R 0.50 WHEELOCK-D RASCHE-R
#> 60: WILLIAMS-J ORPHANIDES-A 3.00 WILLIAMS-J ORPHANIDES-A
#> 61: WILLIAMS-N SARGENT-T 0.50 WILLIAMS-N SARGENT-T
#> 62: WOODFORD-M ROTEMBERG-J 1.00 WOODFORD-M ROTEMBERG-J
#> 63: ZHA-T SARGENT-T 0.50 ZHA-T SARGENT-T
#> 64: ZHA-T WILLIAMS-N 0.50 ZHA-T WILLIAMS-N
#> from to weight Source Target
#> <char> <char> <num> <char> <char>
# Toy example: three authors sign document 1, two sign document 2.
# With fractional counting, a-b gets 1/2 + 1/1 = 1.5
toy <- data.frame(author = c("a", "b", "c", "a", "b"),
paper = c(1, 1, 1, 2, 2))
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 b