Disparity Filter

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, ...)

Arguments

x: A weight matrix, tna object, cograph_network, or igraph object.
level: Significance level (default 0.05). Lower values result in a sparser backbone (fewer edges retained).
...: Additional arguments (currently unused).

Value

For a matrix, an integer matrix of the same dimensions and dimnames with 1 for significant edges and 0 otherwise. For tna, cograph_network and igraph objects, a tna_disparity list with elements significant (the 0/1 matrix), weights_orig, weights_filtered (original weights times the 0/1 matrix), level, n_edges_orig and n_edges_filtered. Any other input raises an error.

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:

$$p = (1 - p_{ij})^{(k_i - 1)}$$

The p-value is computed from the outgoing weights of the source node (row strength and out-degree) and from the incoming weights of the target node (column strength and in-degree). An edge is significant if the smaller of the two p-values is below level. Self-loops are never retained. For igraph input, unweighted edges get weight 1 and multiple edges are summed before filtering.

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.

Examples