# bicm: Bipartite Configuration Model In backbone: Extracts the Backbone from Graphs

 bicm R Documentation

## Bipartite Configuration Model

### Description

`bicm` estimates cell probabilities under the bipartite configuration model

### Usage

``````bicm(M, fitness = FALSE, tol = 1e-08, max_steps = 200, ...)
``````

### Arguments

 `M` matrix: a binary matrix `fitness` boolean: FALSE returns a matrix of probabilities, TRUE returns a list of row and column fitnesses only `tol` numeric, tolerance of algorithm `max_steps` numeric, number of times to run loglikelihood_prime_bicm algorithm `...` optional arguments

### Details

Given a binary matrix M, the Bipartite Configuration Model (BiCM; Saracco et. al. 2015) returns a valued matrix B in which Bij is the approximate probability that Mij = 1 in the space of all binary matrices with the same row and column marginals as M. The BiCM yields the closest approximations of the true probabilities compared to other estimation methods (Neal et al., 2021), and is used by `sdsm()` to extract the backbone of a bipartite projection using the stochastic degree sequence model.

Matrix M is "conforming" if no rows and no columns contain only zeros or only ones. If M is conforming, then `bicm()` is faster. Additionally, if `fitness = TRUE`, then `bicm()` returns a list of row and column fitnesses, which requires less memory. Given the ith row's fitness Ri and the jth column's fitness Rj, the entry Bij in the probability matrix can be computed as Ri x Rj/(1+(Ri x Rj)).

Matrix M is "non-conforming" if any rows or any columns contain only zeros or only ones. If M is non-conforming, then `bicm()` is slower and will only return a probability matrix.

### Value

a matrix of probabilities or a list of fitnesses

### References

package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. PLOS ONE, 17, e0269137. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1371/journal.pone.0269137")}

bicm: Saracco, F., Di Clemente, R., Gabrielli, A., & Squartini, T. (2015). Randomizing bipartite networks: The case of the World Trade Web. Scientific Reports, 5, 10595. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/srep10595")}

### Examples

``````M <- matrix(c(0,0,1,0,1,0,1,0,1),3,3)  #A binary matrix
bicm(M)
``````

backbone documentation built on May 29, 2024, 8:03 a.m.