fdsm | R Documentation |

`fdsm`

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

fdsm( B, alpha = 0.05, trials = NULL, signed = FALSE, mtc = "none", class = "original", narrative = FALSE, progress = TRUE, ... )

`B` |
An unweighted bipartite graph, as: (1) an incidence matrix in the form of a matrix or sparse |

`alpha` |
real: significance level of hypothesis test(s) |

`trials` |
numeric: the number of bipartite graphs generated to approximate the edge weight distribution. If NULL, the number of trials is selected based on |

`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 |

`class` |
string: the class of the returned backbone graph, one of c("original", "matrix", "Matrix", "igraph", "edgelist").
If "original", the backbone graph returned is of the same class as |

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

`progress` |
boolean: TRUE if the progress of Monte Carlo trials should be displayed. |

`...` |
optional arguments |

The `fdsm`

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 *exactly* fixed at their values in `B`

. It uses the `fastball()`

algorithm to generate random
bipartite matrices with give row and column vertex degrees.

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.*

The p-values used to evaluate the statistical significance of each edge are computed using Monte Carlo methods. The number of
`trials`

performed affects the precision of these p-values, and the confidence that a given p-value is less than the
desired `alpha`

level. Because these p-values are proportions (i.e., the proportion of times an edge is weaker/stronger
in the projection of a random bipartite graphs), evaluating the statistical significance of an edge is equivalent to
comparing a proportion (the p-value) to a known proportion (alpha). When `trials = NULL`

, the `power.prop.test`

function
is used to estimate the required number of trials to make such a comparison with a `alpha`

type-I error rate, (1-`alpha`

) power,
and when the riskiest p-value being evaluated is at least 5% smaller than `alpha`

. When any `mtc`

correction is applied,
for simplicity this estimation is based on a conservative Bonferroni correction.

If `alpha`

!= NULL: Binary or signed backbone graph of class `class`

.

If `alpha`

== NULL: An S3 backbone object containing (1) the weighted graph as a matrix, (2) upper-tail p-values as a
matrix, (3, if `signed = TRUE`

) lower-tail p-values as a matrix, (4, if present) node attributes as a dataframe, and
(5) several properties of the original graph and backbone model, from which a backbone can subsequently be extracted
using `backbone.extract()`

.

package: Neal, Z. P. (2022). backbone: An R Package to Extract Network Backbones. *PLOS ONE, 17*, e0269137. doi: 10.1371/journal.pone.0269137

fdsm: 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*. doi: 10.1038/s41598-021-03238-3

fastball: Godard, Karl and Neal, Zachary P. 2022. fastball: A fast algorithm to sample bipartite graphs with fixed degree sequences. *arXiv:2112.04017*#'

#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 <- fdsm(B, alpha = 0.05, trials = 1000, narrative = TRUE, class = "igraph") #An FDSM backbone... plot(bb) #...is sparse with clear communities

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