backbone (version 2.1.0)

fixedcol: Extract backbone using the Fixed Column Model

Description

fixedcol extracts the backbone of a bipartite projection using the Fixed Column Model.

Usage

fixedcol(
  B,
  alpha = 0.05,
  signed = FALSE,
  mtc = "none",
  class = "original",
  narrative = FALSE
)

Value

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

If alpha == NULL: An S3 backbone object containing three matrices (the weighted graph, edges' upper-tail p-values, edges' lower-tail p-values), and a string indicating the null model used to compute p-values, from which a backbone can subsequently be extracted using backbone.extract(). The signed, mtc, class, and narrative parameters are ignored.

Arguments

B

An unweighted bipartite graph, as: (1) an incidence matrix in the form of a matrix or sparse Matrix; (2) an edgelist in the form of a two-column dataframe; (3) an igraph object. Any rows and columns of the associated bipartite matrix that contain only zeros are automatically removed before computations.

alpha

real: significance level of hypothesis test(s)

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 B.

narrative

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

Details

This fixedcol function compares an edge's observed weight in the projection \(B*t(B)\) to the distribution of weights expected in a projection obtained from a random bipartite graph where the column vertex degrees are fixed but the row vertex degrees are allowed to vary.

When signed = FALSE, a one-tailed test (is the weight stronger) is performed for each edge with a non-zero weight. It yields a backbone that perserves edges whose weights are significantly stronger than expected under the null model. When signed = TRUE, a two-tailed test (is the weight stronger or weaker) is performed for each every pair of nodes. It yields a backbone that contains positive edges for edges whose weights are significantly stronger, and negative edges for edges whose weights are significantly weaker, than expected in the chosen null model. NOTE: Before v2.0.0, all significance tests were two-tailed and zero-weight edges were evaluated.

References

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

fixedcol: Neal, Z. P., Domagalski, R., and Sagan, B. (2021). Comparing Alternatives to the Fixed Degree Sequence Model for Extracting the Backbone of Bipartite Projections. Scientific Reports, 11, 23929. tools:::Rd_expr_doi("10.1038/s41598-021-03238-3")

Examples

#A binary bipartite network of 30 agents & 75 artifacts; agents form three communities
B <- rbind(cbind(matrix(rbinom(250,1,.8),10),
                 matrix(rbinom(250,1,.2),10),
                 matrix(rbinom(250,1,.2),10)),
           cbind(matrix(rbinom(250,1,.2),10),
                 matrix(rbinom(250,1,.8),10),
                 matrix(rbinom(250,1,.2),10)),
           cbind(matrix(rbinom(250,1,.2),10),
                 matrix(rbinom(250,1,.2),10),
                 matrix(rbinom(250,1,.8),10)))

P <- B%*%t(B) #An ordinary weighted projection...
plot(igraph::graph_from_adjacency_matrix(P, mode = "undirected",
                                         weighted = TRUE, diag = FALSE)) #...is a dense hairball

bb <- fixedcol(B, alpha = 0.05, narrative = TRUE, class = "igraph") #A fixedcol backbone...
plot(bb) #...is sparse with clear communities