backbone (version 1.4.0)

fixedrow: Compute fixed row sums / hypergeometric backbone probabilities

Description

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

Usage

fixedrow(B)

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.

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: model name, number of rows, skew of row sums, number of columns, skew of column sums, and running time.

Details

Specifically, this 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 row vertex degrees are fixed but the column vertex degrees are allowed to vary.

References

Tumminello, Michele and Miccich<U+00E8>, Salvatore and Lillo, Fabrizio and Piilo, Jyrki and Mantegna, Rosario N. 2011. "Statistically Validated Networks in Bipartite Complex Systems." PLOS ONE, 6(3), 10.1371/journal.pone.0017994

Neal, Zachary. 2013. <U+201C>Identifying Statistically Significant Edges in One-Mode Projections.<U+201D> Social Network Analysis and Mining 3 (4). Springer: 915<U+2013>24. 10.1007/s13278-013-0107-y

Examples

# NOT RUN {
fixedrow_probs <- fixedrow(davis)
# }