backbone (version 2.0.3)

sdsm: Extract backbone using the Stochastic Degree Sequence Model

Description

sdsm extracts the backbone of a bipartite projection using the Stochastic Degree Sequence Model.

Usage

sdsm(
  B,
  method = "RefinedNormal",
  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; (4) a 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.

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", "sparseMatrix", "igraph", "network", "edgelist"). If "original", the backbone graph returned is of the same class as B.

narrative

boolean: TRUE if suggested text & citations should be displayed.

...

optional arguments

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.

Details

The sdsm 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 network where both the row vertex degrees and column vertex degrees are approximately fixed at their values in B. It uses the Bipartite Configuration Model bicm to compute probabilities for the Poisson binomial distribution.

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 in the chosen 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.

References

Neal, Z. P. (2014). The backbone of bipartite projections: Inferring relationships from co-authorship, co-sponsorship, co-attendance, and other co-behaviors. Social Networks, 39, 84-97. 10.1016/j.socnet.2014.06.001 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. 10.1038/s41598-021-03238-3

Examples

# NOT RUN {
#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...
plot(igraph::graph_from_adjacency_matrix(P, mode = "undirected",
                                         weighted = TRUE, diag = FALSE)) #...is a dense hairball

bb <- sdsm(B, alpha = 0.05, narrative = TRUE, class = "igraph") #An SDSM backbone...
plot(bb) #...is sparse with clear communities
# }