fixedcol {backbone}

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,
  missing.as.zero = FALSE,
  signed = FALSE,
  mtc = "none",
  class = "original",
  narrative = FALSE
)

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.

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 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. 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.

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

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. 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