Extracts the statistically significant backbone of a weighted network using the disparity filter method (Serrano, Boguna, & Vespignani, 2009).
Usage
disparity_filter(x, level = 0.05, ...)
# Default S3 method
disparity_filter(x, level = 0.05, ...)
# S3 method for class 'matrix'
disparity_filter(x, level = 0.05, ...)
# S3 method for class 'tna'
disparity_filter(x, level = 0.05, ...)
# S3 method for class 'cograph_network'
disparity_filter(x, level = 0.05, ...)
# S3 method for class 'igraph'
disparity_filter(x, level = 0.05, ...)Value
For matrices: a binary matrix (0/1) indicating significant edges.
For tna, cograph_network, and igraph objects: a tna_disparity object
containing the significance matrix, original weights, filtered weights,
and summary statistics.
Details
The disparity filter identifies edges that carry a disproportionate fraction of a node's total weight, based on a null model where weights are distributed uniformly at random.
For each node \(i\) with degree \(k_i\), and each edge \((i,j)\) with normalized weight \(p_{ij} = w_{ij} / s_i\) (where \(s_i\) is the node's strength), the p-value is:
$$p = (1 - p_{ij})^{(k_i - 1)}$$
Edges are significant if \(p < level\) for either endpoint.
References
Serrano, M. A., Boguna, M., & Vespignani, A. (2009). Extracting the multiscale backbone of complex weighted networks. Proceedings of the National Academy of Sciences, 106(16), 6483-6488.
See also
bootstrap for bootstrap-based significance testing
Examples
# Create a weighted network
mat <- matrix(c(
0.0, 0.5, 0.1, 0.0,
0.3, 0.0, 0.4, 0.1,
0.1, 0.2, 0.0, 0.5,
0.0, 0.1, 0.3, 0.0
), nrow = 4, byrow = TRUE)
rownames(mat) <- colnames(mat) <- c("A", "B", "C", "D")
# Extract backbone at 5% significance level
backbone <- disparity_filter(mat, level = 0.05)
backbone
#> A B C D
#> A 0 0 0 0
#> B 0 0 0 0
#> C 0 0 0 0
#> D 0 0 0 0
# More stringent filter (1% level)
backbone_strict <- disparity_filter(mat, level = 0.01)