sbm: Stochastic Blockmodels

sbm gathers in a single framework the tools to simulate, estimate and represent a variety of stochastic block models (SBM), a family of models that cluster the nodes of a network into blocks sharing the same connectivity patterns.

Supported models

• Emission distributions on the edges: Bernoulli (binary networks), Poisson (counts) and Gaussian (weights).
• Covariates, for simple and bipartite SBM: on the edges, acting on the connectivity, or on the nodes, driving the block memberships.
• Missing values (NA) in the networks: the missing dyads are ignored in the inference (see the help pages for the details of each model).
• Model selection of the number of blocks with the Integrated Classification Likelihood (ICL).
• Graphics with ggplot2: reordered matrices, expected networks, graphons, mesoscopic views and alluvial plots.
• Simulation of networks with sampleSimpleSBM(), sampleBipartiteSBM(), sampleMultipartiteSBM() and sampleMultiplexSBM().

Installation

The stable version is available on CRAN:

install.packages("sbm")

The development version can be installed from GitHub:

# install.packages("pak")
pak::pak("GrossSBM/sbm")

Example

The data set fungusTreeNetwork records the interactions between 154 fungal species and 51 tree species. A bipartite SBM groups the fungi and the trees into blocks sharing the same interaction patterns, the number of blocks being chosen with the ICL.

library(sbm)
data("fungusTreeNetwork")
fungusTree <- fungusTreeNetwork$fungus_tree

fit <- estimateBipartiteSBM(
  fungusTree, model = "bernoulli", dimLabels = c(row = "fungus", col = "tree"),
  estimOptions = list(verbosity = 0, plot = FALSE, nbCores = 1)
)

fit$nbBlocks
#> fungus   tree 
#>      4      4

library(patchwork)
plot(fit, type = "data") + plot(fit, type = "meso")

The vignettes go further: model principles, case studies on simple, bipartite, multipartite and multiplex networks, and covariates on the nodes.

Related packages

• blockmodels: estimation of simple and bipartite SBM (and of dependent multiplex SBM), used by sbm.
• GREMLINS: estimation of multipartite SBM, used by sbm.
• missSBM: SBM for networks with missing data, under various sampling designs (missing at random or not).
• shinySbm: a Shiny application to fit SBM with sbm.

References

• Léger, J.-B. (2016). Blockmodels: A R-package for estimating in Latent Block Model and Stochastic Block Model, with various probability functions, with or without covariates. arXiv:1602.07587.
• Barbillon, P., Donnet, S., Lazega, E. and Bar-Hen, A. (2017). Stochastic block models for multiplex networks: an application to a multilevel network of researchers. Journal of the Royal Statistical Society: Series A, 180(1), 295–314. doi:10.1111/rssa.12193.
• Bar-Hen, A., Barbillon, P. and Donnet, S. (2022). Block models for generalized multipartite networks: Applications in ecology and ethnobiology. Statistical Modelling, 22(4), 273–296. doi:10.1177/1471082X20963254.