Extract Triads with Node Labels

Extract all triads from a network, preserving node labels. This allows users to see which specific node combinations form each motif pattern.

Usage

extract_triads(
  x,
  type = NULL,
  involving = NULL,
  threshold = 0,
  min_total = 5,
  directed = NULL
)

Arguments

x

A matrix, igraph object, tna, or cograph_network

type

Character vector of MAN codes to filter by (e.g., "030T", "030C"). Default NULL returns all types.

involving

Character vector of node labels. Only return triads involving at least one of these nodes. Default NULL returns all triads.

threshold

Minimum edge weight for an edge to be considered present. Type is determined by edges with weight > threshold. Default 0.

min_total

Minimum total weight across all 6 edges. Excludes trivial triads with low overall activity. Default 5.

directed

Logical. Treat network as directed? Default auto-detected.

Value

A data frame with columns:

A, B, C

Node labels for the three nodes in the triad

type

MAN code (003, 012, ..., 300)

weight_AB, weight_BA, weight_AC, weight_CA, weight_BC, weight_CB

Edge weights (frequencies) for all 6 possible directed edges

total_weight

Sum of all 6 edge weights

Details

This function complements motif_census() by showing the actual node combinations that form each motif pattern. A typical workflow is:

1. Use motif_census() to identify over/under-represented patterns

2. Use extract_triads() with type filter to see which nodes form those patterns

3. Sort by total_weight to find the strongest triads

Type vs Weight distinction:

• Type is determined by edge presence (weight > threshold)

• Weights are the actual frequency counts, useful for ranking triads by strength

See also

motifs(), subgraphs(), motif_census(), extract_motifs()

Other motifs: extract_motifs(), get_edge_list(), motif_census(), motifs(), plot.cograph_motif_analysis(), plot.cograph_motifs(), subgraphs(), triad_census()

Examples

# Create a frequency matrix
mat <- matrix(c(
  0, 3, 2, 0,
  0, 0, 5, 1,
  0, 0, 0, 4,
  2, 0, 0, 0
), 4, 4, byrow = TRUE)
rownames(mat) <- colnames(mat) <- c("Plan", "Execute", "Monitor", "Adapt")

net <- as_cograph(mat)

# Extract all triads
triads <- extract_triads(net)
head(triads)
#>         A       B       C type weight_AB weight_BA weight_AC weight_CA
#> 1    Plan Execute Monitor 030T         3         0         2         0
#> 2    Plan Execute   Adapt 030C         3         0         0         2
#> 3    Plan Monitor   Adapt 030C         2         0         0         2
#> 4 Execute Monitor   Adapt 030T         5         0         1         0
#>   weight_BC weight_CB total_weight
#> 1         5         0           10
#> 2         1         0            6
#> 3         4         0            8
#> 4         4         0           10

# Filter by motif type (feed-forward loops only)
ff_loops <- extract_triads(net, type = "030T")

# Filter by node involvement
plan_triads <- extract_triads(net, involving = "Plan")

# Find strongest triads
triads <- extract_triads(net)
strongest <- triads[order(triads$total_weight, decreasing = TRUE), ]