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Tidy Topological Features for One or Many Networks

Source: R/simplicial_features.R
simplicial_features.Rd

Builds a simplicial complex per network and returns its topological summaries as a tidy data.frame – one row per network, one column per feature – ready to use as regression predictors or to join onto unit-level outcomes.

Usage

simplicial_features(
  x,
  threshold = 0,
  max_dim = 4L,
  normalize = FALSE,
  type = "clique"
)

Arguments

x

A netobject, netobject_group, mcml, a square weight matrix, or a named list of any of these. A group or list yields one row per member, an mcml one row per cluster, and a single network one row.

threshold

Minimum absolute edge weight for an edge to exist (passed to build_simplicial). Topology is a step function of this value, so a single threshold is a choice, not a result – pass a vector to sweep it and get one row per network per threshold.

max_dim

Maximum simplex dimension retained. Default 4.

normalize

Divide simplex counts by the number of nodes, so networks of different size are comparable. Default FALSE.

type

Complex type passed to build_simplicial. Default "clique".

Value

A data.frame with one row per network (per threshold), and columns network, threshold, n_nodes, n_edges, b0, b1 (Betti numbers), euler, max_q, d1 ... d<max_dim> (simplex counts by dimension), and higher_order (the total of d2 upward).

Details

Higher-order structure is reported as d2, d3, ... : the number of simplices of that dimension. A 2-simplex is a triangle of three mutually connected states, a 3-simplex a tetrahedron of four. These count co-participation in a dense region, not statistical interaction.

See also

build_simplicial, betti_numbers, q_analysis, outcome_model

Examples

m1 <- matrix(c(0, .6, .5, .6, 0, .4, .5, .4, 0), 3, 3,
             dimnames = list(c("A", "B", "C"), c("A", "B", "C")))
m2 <- matrix(c(0, .2, 0, .2, 0, .1, 0, .1, 0), 3, 3,
             dimnames = list(c("A", "B", "C"), c("A", "B", "C")))
simplicial_features(list(dense = m1, sparse = m2), threshold = 0.3)
#>   network threshold n_nodes n_edges b0 b1 euler max_q d1 d2 d3 d4 higher_order
#> 1   dense       0.3       3       3  1  0     1     2  3  1  0  0            1
#> 2  sparse       0.3       3       0  3  0     3     0  0  0  0  0            0

# Sweep the threshold rather than committing to one.
simplicial_features(list(dense = m1), threshold = c(0.1, 0.3, 0.5))
#>   network threshold n_nodes n_edges b0 b1 euler max_q d1 d2 d3 d4 higher_order
#> 1   dense       0.1       3       3  1  0     1     2  3  1  0  0            1
#> 2   dense       0.3       3       3  1  0     1     2  3  1  0  0            1
#> 3   dense       0.5       3       2  1  0     1     1  2  0  0  0            0