fixedfill {backbone} R Documentation

## Extract backbone using the Fixed Fill Model

### Description

fixedfill extracts the backbone of a bipartite projection using the Fixed Fill Model.

### Usage

fixedfill(
B,
alpha = 0.05,
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. Any rows and columns of the associated bipartite matrix that contain only zeros or only ones 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

The fixedfill 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 number of edges present (i.e., the number of cells filled with a 1) is equal to the number of edges in B. When B is large, this function may be impractically slow and may return a backbone object that contains NaN values.

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.

### 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.

### References

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

fixedfill: 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...