bicm {backbone}R Documentation

Bipartite Configuration Model


bicm estimates cell probabilities under the bipartite configuration model


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



matrix: a binary matrix


boolean: FALSE returns a matrix of probabilities, TRUE returns a list of row and column fitnesses only


numeric, tolerance of algorithm


numeric, number of times to run loglikelihood_prime_bicm algorithm


optional arguments


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.

Optionally (if fitness = TRUE), bicm() instead returns a list of row and column fitnesses, which is faster and requires less memory. Given the ith row's fitness Ri and the jth column's fitness Rj, the entry Bij in the matrix can be computed as Ri\*Rj/(1+(Ri\*Rj)).

Note: M cannot contain any rows or columns that contain all 0s or all 1s.


a matrix of probabilities, or a list of fitnesses


package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. PLOS ONE, 17, e0269137. 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. doi: 10.1038/srep10595


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

[Package backbone version 2.1.0 Index]