Subset repetition statistic for a hyperedge event log

For a focal hyperedge \((t, I, J)\) and orders \((\rho, \ell)\), computes the average activity over every sender subset of I of size rho and every receiver subset of J of size l, per Boschi, Lerner & Wit (2025) Equation 4: $$ \mathrm{subrep}^{\rho,\ell}(t,I,J) = \frac{1}{\binom{|I|}{\rho}\binom{|J|}{\ell}} \sum_{I' \subseteq I,\ |I'|=\rho} \sum_{J' \subseteq J,\ |J'|=\ell} \mathrm{activity}(t, I', J'). $$

Usage

hyperedge_subrep(
  hyperedge_log,
  I,
  J = character(0),
  t,
  rho = length(I),
  l = length(J)
)

Arguments

hyperedge_log

A hyperedge log (see hyperedge_log()).

I

Character vector of senders for the focal event.

J

Character vector of receivers (or character(0) for undirected).

t

Focal time.

rho

Order on the sender side: subset cardinality. Must be between 1 and length(I). Defaults to length(I) (full subset).

l

Order on the receiver side: subset cardinality. Must be between 0 and length(J). Defaults to length(J) (full subset); pass 0 to ignore receivers (undirected).

Value

A single non-negative numeric.

Details

For dyadic events with \(|I| = |J| = 1\), subrep(rho = 1, l = 1) reduces to the dyad event count (already exposed as reciprocity_count and related stats in endogenous_features()). The function exists because for true hyperedge data the average over subsets of intermediate size captures partial-subset repetition that no dyadic statistic can represent.

References

Boschi M, Lerner J, Wit EC (2025). Beyond Linearity and Time- Homogeneity: Relational Hyper Event Models with Time-Varying Non-Linear Effects. arXiv:2509.05289. Lerner J, et al. (2025). The eventnet computation framework.

Examples

hl <- hyperedge_log(
  I    = list(c("a","b"), c("a","c"), c("b","c")),
  J    = list(c("X"),     c("X","Y"), c("Y")),
  time = c(1, 2, 3))
# Activity for the (a, X) sub-pair before t = 4:
hyperedge_activity(hl, I = "a", J = "X", t = 4)
#> [1] 2
# First-order subrep on event (a, b) -> X at t = 4:
hyperedge_subrep(hl, I = c("a","b"), J = "X", t = 4, rho = 1, l = 1)
#> [1] 1.5