Network Motif Analysis

Counts the subgraph classes (motifs) of size 3 or 4 in a network and tests their frequencies against random networks from a null model. Edge weights are ignored, and self-loops and multiple edges are removed before counting.

Usage

motif_census(
  x,
  size = 3,
  n_random = 100,
  method = c("configuration", "gnm"),
  directed = NULL,
  seed = NULL
)

Arguments

x

A matrix, igraph object, or cograph_network.

size

Motif size: 3 (triads) or 4 (tetrads). Default 3.

n_random

Number of random networks for the null model. Must be a whole number of at least 2. Default 100.

method

Null model method. "configuration" (default) rewires the graph with degree-preserving edge swaps. "gnm" draws random graphs with the same numbers of nodes and edges.

directed

Logical or NULL. Whether the network is treated as directed. NULL (default) treats a matrix as directed when it is not symmetric and takes the directedness of an igraph or cograph_network input. A value that conflicts with an igraph or cograph_network input raises an error.

seed

Random seed for reproducibility. Default NULL. When supplied, the caller's RNG state is saved and restored.

Value

A cograph_motifs data frame with one row per motif class and columns:

motif

Motif class name. Directed triads use the 16 MAN codes, undirected triads the classes empty, edge, wedge and triangle, and size 4 the igraph isomorphism class labels M1 to M218 (directed) or M1 to M11 (undirected).

count

Observed number of that motif in the network.

null_mean, null_sd

Mean and standard deviation of the count across the n_random null graphs.

z_score

(count - null_mean) / null_sd. When null_sd = 0, it is 0 if the count equals the null mean and NA otherwise.

p_value

Two-sided empirical permutation p-value with add-one correction, based on the absolute deviation from the null mean.

significant

Logical, p_value < 0.05.

The motif size ("size"), directed flag ("directed"), null-model method ("method"), and number of random networks ("n_random") are stored as attributes.

Details

Printing the result shows the motif table with the null-model settings and the number of over- and under-represented motifs. The result is a data frame and serves as the tidy table directly. plot() on the result is documented in plot-results.

See also

motifs() for the unified API, extract_motifs() for detailed triad extraction, plot-results for plotting

Other motifs: extract_motifs(), extract_triads(), get_edge_list(), motifs(), subgraphs(), triad_census()

Examples

motif_census(regulation_net, n_random = 20, seed = 1)
#> Network Motif Analysis
#> Size: 3-node motifs (directed) | Null: configuration (n=20)
#> 
#>  motif count null_mean  null_sd     z_score   p_value significant
#>    003     7      6.90 2.149663  0.04651891 1.0000000       FALSE
#>    012    27     31.00 4.316431 -0.92669146 0.3809524       FALSE
#>    102     2      8.20 3.721912 -1.66581032 0.1428571       FALSE
#>   021D     9      8.05 2.305029  0.41214235 0.9047619       FALSE
#>   021U    11     10.25 2.788605  0.26895172 0.8571429       FALSE
#>   021C    29     19.70 4.910783  1.89379169 0.1428571       FALSE
#>   111D     9      9.05 2.910507 -0.01717914 1.0000000       FALSE
#>   111U     7      6.20 2.587419  0.30918843 0.8571429       FALSE
#>   030T    11      9.35 3.183427  0.51830928 0.5714286       FALSE
#>   030C     2      3.00 1.521772 -0.65712874 0.7142857       FALSE
#>    201     0      1.25 1.332785 -0.93788572 0.5714286       FALSE
#>   120D     2      1.45 1.190975  0.46180657 0.6190476       FALSE
#>   120U     1      1.50 1.235442 -0.40471361 1.0000000       FALSE
#>   120C     3      3.50 1.147079 -0.43588989 1.0000000       FALSE
#>    210     0      0.60 0.680557 -0.88163072 0.6190476       FALSE
#>    300     0      0.00 0.000000  0.00000000 1.0000000       FALSE
#> 
#> Over-represented: 0 | Under-represented: 0