s-betweenness and s-closeness centrality of hyperedges

Hyperedges become vertices in the unweighted s-line graph: two are adjacent when they share at least s nodes. Betweenness and closeness are then ordinary shortest-path vertex centralities on that graph. At s = 1 these are the paper's hyperedge 1-betweenness and 1-closeness.

Usage

hg_edge_centrality(
  hg,
  s = 1L,
  measure = c("betweenness", "closeness"),
  normalized = TRUE,
  top = NULL,
  start = NULL,
  end = NULL,
  step = NULL,
  window = NULL,
  at = NULL,
  snapshot_mode = c("active", "cumulative"),
  multiedges = TRUE
)

Arguments

hg

A static net_hg or a temporal_hypergraph().

s

One or more positive integer intersection thresholds.

measure

Any of "betweenness" and "closeness".

normalized

Use NetworkX/HypergraphX normalization: undirected betweenness is scaled by 2 / ((n - 1) * (n - 2)), and closeness uses the Wasserman–Faust correction for disconnected line graphs.

top

Optional number of highest-scoring hyperedges to retain per (time, s, measure) group.

start, end, step, window, at

Measurement grid passed to hg_snapshots() when hg is temporal.

snapshot_mode, multiedges

Snapshot mode ("active" or "cumulative") and multi-edge handling passed to hg_snapshots() when hg is temporal.

Value

A tidy data frame with edge, s, measure, and value; temporal input adds a leading time column.

References

Coupette, C., Hartung, D., & Katz, D. M. (2024). Legal hypergraphs. Philosophical Transactions of the Royal Society A, 382(2270), 20230141. doi:10.1098/rsta.2023.0141

Examples

h <- group_hypergraph(
  data.frame(member = c("a", "b", "c", "b", "c", "d"),
             event = rep(c("e1", "e2"), each = 3)),
  "member", "event"
)
hg_edge_centrality(h, s = 1)
#>   edge s     measure value
#> 1   e1 1 betweenness     0
#> 2   e2 1 betweenness     0
#> 3   e1 1   closeness     1
#> 4   e2 1   closeness     1