backbone
Welcome
Thank you for your interest in the backbone package! Here you will find a short example of how to use this package to extract the backbone of a bipartite projection. For more details on these functions and methods, please see our latest manuscript on backbone here:
“Domagalski R, Neal ZP, Sagan B (2021) Backbone: an R package for extracting the backbone of bipartite projections. PLoS ONE 16(1): e0244363.” https://doi.org/10.1371/journal.pone.0244363
For additional resources on how to use the backbone package, please see www.rbackbone.net
The Backbone of a Graph
The backbone package 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)),
hypergeometric model (Neal, Z.
(2013)), the fixed degree
sequence model (Zweig, K. A., and Kaufmann, M.
(2011)), a fixed column
model, a fixed fill model, as well as a universal threshold method.
In a graph G, edges are either present (i.e. G_{ij}=1) or absent
(i.e. G_{ij}=0). However in a weighted or valued graph, edges can take
a range of values that may capture such properties as the strength or
capacity of the edge. Although weighted graphs contain a large amount of
information, there are some cases (e.g. visualization, application of
statistical models not developed for weighted graphs) where it is useful
to reduce this information by focusing on an unweighted subgraph that
contains only the most important edges. We call this subgraph the
backbone of G, which we denote as G’. Extracting G’ from G
requires deciding which edges to preserve. This usually involves
selecting a threshold T_{ij} such that edges are preserved if they are
above the threshold (i.e. G_{ij}’=1 if G_{ij} > T_{ij}), and omitted
if they are below the threshold (i.e. G_{ij}’=0 if G_{ij} < T_{ij}).
It is also possible to extract a signed backbone by selecting upper
T_{ij} and lower T’_{ij} thresholds such that G_{ij}’=1 if
G_{ij}>T_{ij}, G_{ij}’=-1 if G_{ij} < T’_{ij}, and G_{ij}’=0 if
G_{ij} > T’_{ij} and G_{ij} < T_{ij}. The key to all backbone
extraction methods lies in the selection of T. The backbone package
provides several different methods for selecting T and thus extracting
G’ from G.
The backbone package specifically provides five different ways of
selecting T if the graph G is a bipartite projection. That is, G =
BB^T where B is a bipartite graph. To decide whether an edge of a
bipartite projection G is statistically significant, we compare the
edge’s observed weight to the distribution of weights expected in a
projection obtained from a random bipartite graph under a null model.
Given a null model that can generate a distribution of an edge’s
weights, we can then compute the probability that the observed weight is
in the upper or lower tail of that distribution. The backbone package
provides several different null models to use, all of which define
different constraints on the row degrees and column degrees of a random
bipartite graph in their corresponding distribution. The options are:
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. Here the expected row and column degrees of a random bipartite graph in the distribution match that of the original bipartite graph.fixedrow(): computes the probability of edge weights being above or below the observed edge weights in a bipartite projection using the hypergeometric model. Here the row degrees of a random bipartite graph in the distribution exactly match that of the original bipartite graph. The column degrees are allowed to vary.fixedcol(): computes the probability of edge weights being above or below the observed edge weights in a bipartite projection using the Poisson binomial model. Here the column degrees of a random bipartite graph in the distribution exactly match that of the original bipartite graph. The row degrees are allowed to vary.fdsm(): computes the proportion of edge weights above or below the observed edge weights in a bipartite projection using the fixed degree sequence model. Here the row and column degrees of a random bipartite graph in the distribution exactly match that of the original bipartite graph.fixedfill():computes the probability of edge weights being above or below the observed edge weights in a bipartite projection where the number of edges in a random bipartite graph of the distribution exactly match the number of edges of the original bipartite graph.
Once one of these models is computed, use to return the backbone graph for a chosen alpha value.
Installation
You can install the released version of backbone from CRAN with:
install.packages("backbone")You can install from GitHub with:
library(devtools)
install_github("domagal9/backbone", build_vignettes = TRUE)Example
This is a basic example which shows you how to solve a common problem using the included Davis’ Southern Women dataset. We can now decide which null model to compare the observed projection to.
Let’s compare our bipartite graph to the distribution of bipartite
graphs where the expected row and column sums match our data. This is
the sdsm() function.
library(backbone)
#> ____
#> | _ \ backbone v1.4.0
#> |#|_) | Cite: Domagalski, R., Neal, Z. P., & Sagan, B. (2021). Backbone: An
#> |# _ < R package for extracting the backbone of bipartite projections.
#> |#|_) | PLoS ONE. https://doi.org/10.1371/journal.pone.0244363
#> |____/ For help: type vignette("backbone"); email zpneal@msu.edu; github domagal9/backbone
data(davis)
null_model_probabilities <- sdsm(davis)
#> This matrix object looks like an unweighted bipartite network of 18 agents and 14 artifacts.
backbone <- backbone.extract(null_model_probabilities, signed = TRUE, alpha = 0.05)For more detailed examples and background on the topic, see
vignette("backbone_introduction", package = "backbone") or our
manuscript on the backbone package:
https://doi.org/10.1371/journal.pone.0244363