Correlation of hyperdegrees across interaction orders

For every pair of hyperedge sizes \(s < t\) present in the hypergraph, the Pearson correlation across nodes between the size-\(s\) hyperdegree (the number of size-\(s\) hyperedges containing the node) and the size-\(t\) hyperdegree, as reported by Lotito et al. (2023) for the high-school contact hypergraph (\(\rho_{2,3}\), \(\rho_{2,4}\), \(\rho_{3,4}\)). A high value means that nodes active in pairs are also active in larger groups.

Usage

hg_degree_correlation(hg)

Arguments

hg: A hypernets net_hg, dense or sparse.

Value

A base data.frame, one row per pair of present hyperedge sizes size_1 < size_2, with columns size_1, size_2, correlation (Pearson, NA when undefined) and n_nodes.

Details

Every node of hg enters every correlation (with degree 0 at the sizes it does not take part in). Sizes below two are ignored, as in hypergraphx. A pair is NA when one of the two sequences is constant. hypergraphx 1.8.0 degree_correlation() returns the full (max_size - 1)-square matrix, including sizes with no hyperedge (all NaN); hypernets returns one row per pair of sizes that occur. Tested against hypergraphx at 1e-12.

Conditions

Raises hypernets_bad_input when hg is not a net_hg or has fewer than two distinct hyperedge sizes of at least two.

References

Lotito, Q. F., Contisciani, M., De Bacco, C., Di Gaetano, L., Gallo, L., Montresor, A., Musciotto, F., Ruggeri, N., & Battiston, F. (2023). Hypergraphx: a library for higher-order network analysis. Journal of Complex Networks, 11(3), cnad019. doi:10.1093/comnet/cnad019

Examples

groups <- data.frame(
  member = c("a", "b", "a", "c", "b", "c", "a", "d",
             "a", "b", "c", "a", "b", "d", "c", "d", "e"),
  group  = c("p1", "p1", "p2", "p2", "p3", "p3", "p4", "p4",
             "t1", "t1", "t1", "t2", "t2", "t2", "t3", "t3", "t3")
)
hg <- group_hypergraph(groups, actor = "member", group = "group")
hg_degree_correlation(hg)
#>   size_1 size_2 correlation n_nodes
#> 1      2      3   0.7844645       5