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Structural measures for a hypergraph

Source: R/hypergraph_measures.R, R/text_verbs.R
hg_measures.Rd

Computes a comprehensive structural-statistics suite for a net_hg: node-level, hyperedge-level, and global measures. All measures are derived in a few BLAS calls on the incidence matrix.

Usage

# S3 method for class 'net_hg_measures'
print(x, ...)

hg_measures(
  hg,
  what = c("nodes", "edges", "overlap", "summary", "distribution", "components"),
  measure = c("hyperdegree", "strength", "n_neighbors", "size")
)

Arguments

x

A hg_measures object.

...

Additional arguments (ignored).

hg

A text_hypergraph() (or any hypernets net_hg).

what

Which table: "nodes" (default; one row per node with hyperdegree, strength, max_edge_size and n_neighbors, the distinct nodes it shares a hyperedge with), "edges" (one row per hyperedge with its size), "overlap" (one row per hyperedge pair with overlap, overlap_coefficient, jaccard), "summary" (one row per scalar measure), "distribution" (the empirical distribution of measure, as a hypernets_distribution table whose plot() draws the CCDF), or "components" (one row per connected component through shared hyperedges, with its n_nodes, n_edges, share of nodes and diameter).

measure

For what = "distribution": "hyperdegree" (default), "strength", "n_neighbors" (node measures) or "size" (hyperedge cardinality).

Value

The input x invisibly.

A base data.frame, one row per node, edge, edge pair, measure, distinct value, or component according to what.

Details

what = selects which table is returned, as a tidy data.frame.

All measures are computed via standard matrix operations on the binary incidence \(B = (b_{ij})\) where \(b_{ij} = 1\) iff node \(i\) is in hyperedge \(j\):

  • hyperdegree = rowSums(B), edge_sizes = colSums(B)

  • co_degree = tcrossprod(B) (with zero diagonal)

  • edge_pairwise_overlap = crossprod(B) (with zero diagonal)

  • overlap_coefficient[i, j] = overlap[i, j] / min(edge_sizes[i], edge_sizes[j])

  • jaccard[i, j] = overlap[i, j] / (edge_sizes[i] + edge_sizes[j] - overlap[i, j])

Empty hypergraph (n_hyperedges == 0) returns trivial zeros and empty matrices.

References

Lee, G., Bu, F., Eliassi-Rad, T., & Shin, K. (2025). A survey on hypergraph mining: patterns, tools, and generators. ACM Computing Surveys, 57(8), 203. doi:10.1145/3719002

Do, M. T., Yoon, S., Hooi, B., & Shin, K. (2020). Structural patterns and generative models of real-world hypergraphs. arXiv:2006.07060.

See also

network_hypergraph(), group_hypergraph(), hg_clique_expansion().

Examples

hg <- text_hypergraph(c(
  a = "salt and soup and onions",
  b = "soup and salt",
  c = "stars and sky"
))
hg_measures(hg)
#>   node hyperdegree strength max_edge_size n_neighbors
#> 1    a           4        8             3           2
#> 2    b           3        7             3           2
#> 3    c           3        5             3           2
hg_measures(hg, what = "summary")
#>                  measure     value
#> 1                n_nodes 3.0000000
#> 2           n_hyperedges 6.0000000
#> 3                density 0.5555556
#> 4          avg_edge_size 1.6666667
#> 5 pairwise_participation 1.0000000
hg_measures(hg, what = "components")
#>   component n_nodes n_edges share diameter
#> 1         1       3       6     1        1