Hyper-event dominance — hyperevent

Dominance among authors based on the hyper-event chain Author -> Citing paper -> Cited paper -> Author (Espinosa-Rada, 2026).

Usage

hyperevent_dominance(
  X,
  W,
  Xb = X,
  tau = 2,
  dimensions = c("authored", "cited_papers", "cited_authors"),
  closed = c(FALSE, TRUE, TRUE),
  strict = c("asymmetric", "proper"),
  closure_papers = c("citing", "authored"),
  max_authors = NULL,
  team_size = NULL,
  direction = c("dominated", "dominates")
)

Arguments

X: An incidence matrix of authors (rows) and the citing papers they authored (columns)
W: A square citation matrix where W[p, q] = 1 if paper p cites paper q
Xb: An incidence matrix of authors and the cited papers they authored. By default, the same as X
tau: Minimum number of dimensions in which an author should be weakly dominated
dimensions: The dimensions to be considered: authored, cited_papers and/or cited_authors
closed: A logical vector with whether the neighbourhoods of authored, cited_papers and cited_authors are closed
strict: Whether the strict dominance is asymmetric (default) or a proper inclusion
closure_papers: Whether the closed neighbourhood of cited papers adds the citing papers of the author (default) or every paper authored
max_authors: If not NULL, the citing papers with more authors than this number are excluded
team_size: Number of authors of each paper, in the same order as the columns of X. By default, the column sums of X
direction: Whether D[u, v] = 1 means that u is dominated by v (default) or that u dominates v, as in the figures of Espinosa-Rada (2026)

Value

This function returns a binary dominance matrix D of the authors.

Details

Each author has three neighbourhoods built from the hyper-events in which the author wrote the citing paper:

(authored) productive participation: the citing papers authored, \(X\),

(cited_papers) citation reach: the cited papers, \(X \circ W\). Its closed version adds the papers authored,

(cited_authors) recognition: the cited authors, \(X \circ W \circ X_b^T\). Its closed version adds the author itself.

Author \(a_i\) dominates \(a_j\) when the neighbourhood of \(a_j\) is included in the (closed) neighbourhood of \(a_i\) in at least tau dimensions, and the dominance is strict in at least one dimension (see pareto_dominance()). Authors without hyper-events are excluded.

The defaults reproduce the analysis of Espinosa-Rada (2026): the three dimensions, open neighbourhoods for the authored papers and closed neighbourhoods for the cited papers and authors, and asymmetric strict dominance. The alternatives are:

strict = "proper" follows the formal definition of strict dominance as proper inclusion, \(N_k(a_j) \subsetneq N^*_k(a_i)\). As closed neighbourhoods add elements to \(a_i\), proper inclusion is less demanding than the asymmetric criterion, where \(a_i\) should not be included in \(a_j\). With proper inclusion, two authors might dominate each other, so the relation is not always a partial order. The same might happen with the asymmetric criterion when tau = 1, if each author dominates the other in a different dimension.

closure_papers sets which papers of \(a_i\) are added to close the neighbourhood of cited papers. With "citing" (default, as in the analysis scripts of the article) they are the citing papers of \(a_i\) with hyper-events. With "authored" they are every paper authored by \(a_i\), in X or in Xb, as in the text of Section 3.5, so that a paper of \(a_i\) cited by \(a_j\) is in the closed neighbourhood of \(a_i\) even when it does not cite other papers of the corpus.

max_authors excludes the citing papers of large teams before computing the neighbourhoods, as a robustness check for consortium papers (in the article, papers with more than 20 authors). As the matrices might only contain some of the authors of each paper (e.g. a bounded population), the number of authors can be given in team_size.

References

Espinosa-Rada, A. (2026). Network positions within scholars and intellectual networks. Journal of Informetrics, 20, 101854. doi:10.1016/j.joi.2026.101854

Schoch, D. and Brandes, U. (2016). Re-conceptualizing centrality in social networks. European Journal of Applied Mathematics, 27(6), 971–985. doi:10.1017/S0956792516000401

Author

Alejandro Espinosa-Rada

Examples

X <- matrix(c(
  1, 1, 1, 0,
  1, 1, 0, 0,
  1, 0, 0, 0,
  0, 1, 0, 0,
  0, 0, 1, 1
), byrow = TRUE, ncol = 4)
rownames(X) <- c("a1", "a2", "a3", "a4", "a5")
colnames(X) <- c("w1", "w2", "w3", "w4")

W <- matrix(c(
  0, 1, 1, 0,
  0, 0, 1, 0,
  0, 0, 0, 1,
  0, 0, 0, 0
), byrow = TRUE, ncol = 4)
rownames(W) <- colnames(X)
colnames(W) <- colnames(X)

hyperevent_dominance(X, W, tau = 2)
#>    a1 a2 a3 a4 a5
#> a1  0  0  0  0  0
#> a2  1  0  0  0  0
#> a3  1  1  0  0  0
#> a4  1  1  1  0  0
#> a5  1  0  0  0  0
hyperevent_dominance(X, W, tau = 2, strict = "proper")
#>    a1 a2 a3 a4 a5
#> a1  0  0  0  0  0
#> a2  1  0  1  0  0
#> a3  1  1  0  0  0
#> a4  1  1  1  0  0
#> a5  1  0  0  0  0
hyperevent_dominance(X, W, tau = 1, dimensions = c("authored", "cited_authors"))
#>    a1 a2 a3 a4 a5
#> a1  0  0  0  0  0
#> a2  1  0  0  0  0
#> a3  1  1  0  0  0
#> a4  1  1  1  0  0
#> a5  1  1  1  1  0