backbone (version 1.5.1)

fixedcol: Compute fixed column sums / Poisson binomial backbone probabilities

Description

`fixedcol` computes the probability of observing a higher or lower edge weight using the Poisson binomial distribution. Once computed, use backbone.extract to return the backbone matrix for a given alpha value.

Usage

fixedcol(B, method = "RefinedNormal")

Arguments

B

graph: An unweighted bipartite graph object of class matrix, sparse matrix, igraph, edgelist, or network object. Any rows and columns of the associated bipartite matrix that contain only zeros are automatically removed before computations.

method

string: Specifies the method of the Poisson Binomial distribution computation used by the "ppbinom" function in PoissonBinomial-Distribution. "RefinedNormal" gives quick, very accurate approximations, while "DivideFFT" gives the quickest exact computations.

Value

backbone, a list(positive, negative, summary). Here `positive` is a matrix of probabilities of edge weights being equal to or above the observed value in the projection, `negative` is a matrix of probabilities of edge weights being equal to or below the observed value in the projection, and `summary` is a data frame summary of the inputted matrix and the model used including: class, model name, number of rows, number of columns, and running time.

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.

References

Neal, Domagalski, and Sagan. 2021. "Comparing Models for Extracting the Backbone of Bipartite Projections." arXiv:2105.13396 cs.SI)

Examples

# NOT RUN {
fixedcol(davis)
# }