Provides methods for extracting from a weighted graph a binary or signed backbone that retains only the significant edges. The user may input a weighted graph, or a bipartite graph from which a weighted graph is first constructed via projection. Backbone extraction methods include:
the stochastic degree sequence model (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, Elsevier: 84-97.),
hypergeometric model (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. DOI:10.1007/s13278-013-0107-y.),
the fixed degree sequence model (Zweig, Katharina Anna, and Michael Kaufmann. 2011. <U+201C>A Systematic Approach to the One-Mode Projection of Bipartite Graphs.<U+201D> Social Network Analysis and Mining 1 (3): 187<U+2013>218.),
as well as a universal threshold method.
Some features of the package are:
'universal': returns a backbone graph in which edge weights
are set to 1 if above the given upper parameter threshold,
and set to -1 if below the given lower parameter threshold, and are 0 otherwise.
'sdsm': computes the probability of edge weights being above or below the observed edge weights in a bipartite projection using the stochastic degree sequence model.
Once computed, use backbone.extract to return the backbone matrix for a given alpha value.
'hyperg': computes the probability of edge weights being above or below the observed edge weights in a bipartite projection using the hypergeometric model.
Once computed, use backbone.extract to return the backbone matrix for a given alpha value.
'fdsm': computes the proportion of edge weights above or below the observed edge weights in a bipartite projection using the fixed degree sequence model.
Once computed, use backbone.extract to return the backbone matrix for a given alpha value.
'backbone.extract': returns a backbone graph object that retains only the significant edges.
Additional functions that aid in the use of the above models are exported:
'polytope': finds a matrix that maximizes the entropy function, used in sdsm.
'curveball': generates a random 0/1 matrix with the same row and column sums as the input, used in sdsm and fdsm.
For additional documentation and background on the package functions, see vignette("backbone", package = "backbone").