Growth of a temporal hypergraph over time — hg

Counts, on a measurement grid, the nodes and hyperedges present in the temporal hypergraph: the descriptive time series of Coupette et al. (2024, Figures 4a and 5b). Hyperedges are counted twice, as they are (n_edges, the multi-hypergraph) and as distinct member sets (n_edges_distinct, the binary hypergraph), so the two representations of the paper's Table 2 can be read against each other over time.

Usage

hg_growth(
  x,
  start = NULL,
  end = NULL,
  step = NULL,
  window = NULL,
  at = NULL,
  mode = c("active", "cumulative"),
  components = FALSE
)

# S3 method for class 'hypernets_series'
plot(x, columns = NULL, facets = TRUE, ...)

Arguments

x: A hypernets_series table (for plot).
start, end: Bounds of the measured period, as numbers on the hypergraph's clock or dates for a calendar hypergraph. Default: the observation window.
step: How often to measure, in the hypergraph's time unit. NULL (default) measures at every event time.
window: How much time each measurement covers. Defaults to step when a step is given (a partition of the period) and to 0 otherwise (a point sample); larger than step gives a rolling window; "all" measures the whole period as one window.
at: Instants to measure instead of a grid; may be a vector.
mode: "active" (default) or "cumulative", see Description. The former "all" is deprecated: it is "cumulative" with at unset.
components: Also report the connectivity of the measured hypergraph at each time: the number of connected components, the share of its nodes in the largest, and its diameter (longest shortest path between two nodes sharing a chain of hyperedges)? Default FALSE; the computation is a breadth-first search per node and time.
columns: Which numeric columns to draw; default all but time.
facets: Draw one panel per column (default TRUE, because node and hyperedge counts live on different scales) or all columns in one panel with a legend.
...: Unused; for S3 consistency.

Value

A base data.frame of class hypernets_series, one row per window, with time (the window start on the hypergraph's clock), n_nodes, n_edges, n_edges_distinct, n_memberships, and for mode = "active" also n_nodes_cumulative, n_edges_cumulative and n_edges_distinct_cumulative. With components = TRUE, further n_components, largest_component (share of active nodes) and diameter. plot() draws each count against time, on the calendar when the hypergraph has one.

For plot, a ggplot object.

Details

mode = "active" counts what each window measures – an interval hyperedge active in it, a contact hyperedge occurring in it – and adds the _cumulative columns, the hyperedges begun by the end of the window, the static aggregate that a point-aggregation model would report. mode = "cumulative" reports only that growing view, and then counts a node from its own entry time when the constructor received a node table with a start column, otherwise from the first hyperedge that contains it.

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

seats <- data.frame(
  case = rep(c("A", "B", "C"), each = 3),
  arbitrator = c("p1", "a1", "a2", "p2", "a1", "a3", "p1", "a4", "a5"),
  constituted = rep(c(1, 2, 4), each = 3), concluded = rep(c(4, 3, 6), each = 3)
)
thg <- temporal_hypergraph(seats, actor = "arbitrator", group = "case",
                           start = "constituted", end = "concluded")
growth <- hg_growth(thg)
growth
#>   time n_nodes n_edges n_edges_distinct n_memberships n_nodes_cumulative
#> 1    1       3       1                1             3                  3
#> 2    2       5       2                2             6                  5
#> 3    3       5       2                2             6                  5
#> 4    4       5       2                2             6                  7
#> 5    6       3       1                1             3                  7
#>   n_edges_cumulative n_edges_distinct_cumulative
#> 1                  1                           1
#> 2                  2                           2
#> 3                  2                           2
#> 4                  3                           3
#> 5                  3                           3
plot(growth)

# a regular grid: every two steps, each window two steps wide
hg_growth(thg, step = 2)
#>   time n_nodes n_edges n_edges_distinct n_memberships n_nodes_cumulative
#> 1    1       5       2                2             6                  5
#> 2    3       7       3                3             9                  7
#> 3    5       3       1                1             3                  7
#>   n_edges_cumulative n_edges_distinct_cumulative
#> 1                  2                           2
#> 2                  3                           3
#> 3                  3                           3