disparity {backbone}

Extract backbone using the Disparity Filter

Description

disparity extracts the backbone of a weighted network using the Disparity Filter.

Usage

disparity(
  W,
  alpha = 0.05,
  missing.as.zero = FALSE,
  signed = FALSE,
  mtc = "none",
  class = "original",
  narrative = FALSE
)

Arguments

W

A positively-weighted unipartite graph, as: (1) an adjacency matrix in the form of a matrix or sparse Matrix; (2) an edgelist in the form of a three-column dataframe; (3) an igraph object.

alpha

real: significance level of hypothesis test(s)

missing.as.zero

boolean: should missing edges be treated as edges with zero weight and tested for significance

signed

boolean: TRUE for a signed backbone, FALSE for a binary backbone (see details)

mtc

string: type of Multiple Test Correction to be applied; can be any method allowed by p.adjust.

class

string: the class of the returned backbone graph, one of c("original", "matrix", "Matrix", "igraph", "edgelist"). If "original", the backbone graph returned is of the same class as W.

narrative

boolean: TRUE if suggested text & citations should be displayed.

Details

The disparity function applies the disparity filter (Serrano et al., 2009), which compares an edge's weight to its expected weight if a node's total degree was uniformly distributed across all its edges. The graph may be directed or undirected, however the edge weights must be positive.

When signed = FALSE, a one-tailed test (is the weight stronger?) is performed for each edge. The resulting backbone contains edges whose weights are significantly stronger than expected in the null model. When signed = TRUE, a two-tailed test (is the weight stronger or weaker?) is performed for each edge. The resulting backbone contains positive edges for those whose weights are significantly stronger, and negative edges for those whose weights are significantly weaker, than expected in the null model.

If W is an unweighted bipartite graph, then the disparity filter is applied to its weighted bipartite projection.

Value

If alpha != NULL: Binary or signed backbone graph of class class.

If alpha == NULL: An S3 backbone object containing (1) the weighted graph as a matrix, (2) upper-tail p-values as a matrix, (3, if signed = TRUE) lower-tail p-values as a matrix, (4, if present) node attributes as a dataframe, and (5) several properties of the original graph and backbone model, from which a backbone can subsequently be extracted using backbone.extract().

References

package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. PLOS ONE, 17, e0269137. doi:10.1371/journal.pone.0269137

disparity filter: Serrano, M. A., Boguna, M., & Vespignani, A. (2009). Extracting the multiscale backbone of complex weighted networks. Proceedings of the National Academy of Sciences, 106, 6483-6488. doi:10.1073/pnas.0808904106

Examples

#A network with heterogeneous (i.e. multiscale) weights
net <- matrix(c(0,10,10,10,10,75,0,0,0,0,
                10,0,1,1,1,0,0,0,0,0,
                10,1,0,1,1,0,0,0,0,0,
                10,1,1,0,1,0,0,0,0,0,
                10,1,1,1,0,0,0,0,0,0,
                75,0,0,0,0,0,100,100,100,100,
                0,0,0,0,0,100,0,10,10,10,
                0,0,0,0,0,100,10,0,10,10,
                0,0,0,0,0,100,10,10,0,10,
                0,0,0,0,0,100,10,10,10,0),10)

net <- igraph::graph_from_adjacency_matrix(net, mode = "undirected", weighted = TRUE)
plot(net, edge.width = sqrt(igraph::E(net)$weight)) #A stronger clique & a weaker clique

strong <- igraph::delete.edges(net, which(igraph::E(net)$weight < mean(igraph::E(net)$weight)))
plot(strong) #A backbone of stronger-than-average edges ignores the weaker clique

bb <- disparity(net, alpha = 0.05, narrative = TRUE) #A disparity backbone...
plot(bb) #...preserves edges at multiple scales