Package {easybgm}

Type:	Package
Title:	Extracting and Visualizing Bayesian Graphical Models
Version:	0.5.0
Maintainer:	Karoline Huth <k.huth@uva.nl>
Description:	Fit and visualize the results of a Bayesian analysis of networks commonly found in psychology. The package supports cross-sectional network models for ordinal, binary, continuous, and mixed data, fitted using the packages 'bgms' (default), 'BDgraph', and 'BGGM', as well as network comparison tests fitted using the packages 'bgms' and 'BGGM'. The package provides the parameter estimates, posterior inclusion probabilities, inclusion Bayes factor, and the posterior density of the parameters. In addition, for 'BDgraph' and 'bgms' it allows to assess the posterior structure space. Furthermore, the package comes with an extensive suite for visualizing results.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
URL:	https://github.com/KarolineHuth/easybgm
BugReports:	https://github.com/KarolineHuth/easybgm/issues
Encoding:	UTF-8
Depends:	R (≥ 4.1.0)
Imports:	BDgraph, BGGM, bgms (≥ 0.1.6.3), dplyr, ggplot2, HDInterval, qgraph, coda
Suggests:	testthat (≥ 3.2.3)
Config/testthat/edition:	3
Config/roxygen2/version:	8.1.0
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2026-09-10 11:02:27 UTC; karolinehuth
Author:	Karoline Huth [aut, cre], Sara Keetelaar [ctb], Nikola Sekulovski [ctb], Gali Geller [ctb]
Repository:	CRAN
Date/Publication:	2026-09-10 11:30:02 UTC

Plot of interaction parameters and their 95% highest density intervals

Description

Plots the 95% highest density interval of the posterior distribution of the parameter estimates. The plot can be used to visualize the uncertainty of the partial association estimates. The x-axis indicates the strength of the partial association. The y-axis indicates the edge between nodes $i$ and $j$. The farther the posterior estimates (i.e., the points in the plot) are from zero, the stronger the partial association of the edge. The wider the highest density intervals (i.e., the error bar around the point), the less certain we are about the strength of the association.

Usage

plot_parameterHDI(output, ...)

Arguments

Value

Returns a plot

Examples

## Not run: 

library(easybgm)
library(bgms)


data <- na.omit(Wenchuan)
fit <- easybgm(data[1:50, 1:5], type = "ordinal",
              iter = 100,    # for demonstration only
              edge_selection = TRUE, save = TRUE)
plot_parameterHDI(fit)

## End(Not run)

Extract the results of a Bayesian analysis of networks

Description

Extract the results of a Bayesian analysis of networks

Usage

bgm_extract(fit, ...)

Arguments

Fit a Bayesian analysis of networks

Description

Fit a Bayesian analysis of networks

Usage

bgm_fit(fit, ...)

Arguments

Plot strength centralities and 95% highest density interval

Description

Visualize the strength centralities and their uncertainties. The centrality estimate can be obtained for each sample of the posterior distribution of the association parameters to obtain an estimate of the uncertainty of the strength centrality estimate.

Usage

plot_centrality(output, group_names = NULL, ...)

Arguments

Value

Returns a plot

Examples

## Not run: 
library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)
fit <- easybgm(data[1:50, 1:5], type = "ordinal",
                iter = 100,    # for demonstration only
                edge_selection = TRUE, save = TRUE,
                centrality = TRUE)

plot_centrality(fit)

## End(Not run)

Test whether a network splits into clusters

Description

For a network fitted with the Stochastic Block Model (SBM) edge prior, this gives a Bayes factor for the number of clusters. With type = "complement" it weighs more than one cluster against exactly one; with type = "point" it weighs b1 clusters against b2. Values above 1 favour the first of the two; take the reciprocal to read the evidence the other way round.

Usage

clusterBayesfactor(fit, type = "complement", b1 = NULL, b2 = NULL)

Arguments

Details

The count is the number of clusters the model has available, which can be larger than the number that actually hold variables, since a cluster may come out empty. For the memberships themselves, see bgms::extract_sbm(). Evidence for clustering concerns the network's edge structure and is not by itself evidence of multidimensionality.

Value

A single unrounded Bayes factor. NA with a warning if neither point hypothesis appears in the posterior. A result of 0 or Inf means the sampler never visited one of the two, so run more iterations rather than reading it as decisive.

Plot posterior complexity probabilities

Description

Plots the posterior complexity probabilities of all visited structures, where complexity comprises the network density.

Usage

plot_complexity_probabilities(output, ...)

Arguments

Value

Returns a plot

Examples

## Not run: 

library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)[1:50, 1:5]
fit <- easybgm(data, type = "ordinal", save = TRUE, edge_selection = TRUE,
                iter = 100   # for demonstration only
                )

plot_complexity_probabilities(fit)

## End(Not run)

Bayesian analysis of networks

Description

Easy estimation of a Bayesian graphical models to obtain conditional (in)dependence relations between variables in a network.

Usage

easybgm(
  data,
  type,
  package = NULL,
  save = FALSE,
  centrality = FALSE,
  iter = 1000,
  progress = TRUE,
  baseline_category = NULL,
  not_cont = NULL,
  ...
)

Arguments

Details

Data types and package support

BGGM and BDgraph fit continuous, mixed, ordinal and binary data; the Blume-Capel model and per-variable type vectors are fitted only by bgms. "Default" marks the package used when package is left unspecified. Because bgms 0.1.6.3 cannot fit continuous data, the bgms column is split by version:

Prior specification

Users may wish to deviate from the default (uninformative) prior specifications. This can be done by passing additional arguments via ... to the fitting function of the chosen package. We give an overview of the available prior arguments per package below.

bgms (>= 0.2.0.0) uses prior-constructor objects from the bgms package. Pass them through ...:

• interaction_prior: A parameter prior on pairwise interactions. Use normal_prior(scale) (default normal_prior(scale = 1)), cauchy_prior(scale), or beta_prime_prior(alpha, beta). For example, a cauchy prior with scale 1 would be specified with adding the argument interaction_prior = cauchy_prior(1) to the easybgm call.

• threshold_prior: A parameter prior on threshold (main effect) parameters. Use beta_prime_prior(alpha, beta) (default beta_prime_prior(0.5, 0.5)), cauchy_prior(scale), or normal_prior(scale). For example, a cauchy prior with scale 1 would be specified with adding the argument threshold_prior = cauchy_prior(1) to the easybgm call.

• means_prior: A prior on the means of continuous variables in mixed MRF models. Default normal_prior(scale = 1), specify with means_prior = normal_prior(scale = 1).

• precision_scale_prior: A prior on the diagonal entries of the precision matrix (GGM and mixed MRF). Use exponential_prior(rate) (default exponential_prior(eta = 1)) or gamma_prior(shape, rate), for example, specified as precision_scale_prior = exponential_prior(1)

• precision_graph_prior: How the graph prior is applied to the precision matrix (GGM and mixed MRF). Either "hierarchical" (the default), which tracks the normalizing constant, or "joint".

• edge_prior: An indicator prior on edge inclusion. Use bernoulli_prior(inclusion_probability) (default bernoulli_prior(0.5); inclusion_probability can also be a symmetric p \times p matrix of edge-specific probabilities), beta_bernoulli_prior(alpha, beta), or sbm_prior(alpha, beta, alpha_between, beta_between, dirichlet_alpha, lambda) for the Stochastic Block Model prior. For example, a bernoulli prior with prior probabilit of 0.5 would be specified with adding the argument edge_prior = bernoulli_prior(0.5) to the easybgm call.

For backwards compatibility of bgms (< 0.2.0.0), the previous prior specifications are still accepted and translated into the relevant constructs. Check the previous bgms version for its prior arguments.

BDgraph:

• df.prior: Degrees of freedom of the prior G-Wishart distribution on the precision matrix. Default is 3.

• g.prior: Prior probability of edge inclusion. Can be a scalar (same for all edges) or a matrix (edge-specific). This can also be a symmetric pxp matrix of edge-specific inclusion probabilities. Default is 0.5.

BGGM:

• prior_sd: Standard deviation of the prior on interaction parameters (approximately the scale of a beta distribution). Default is 0.25.

We encourage researchers to conduct prior sensitivity checks.

Value

An object of class easybgm containing the following elements:

Always returned:

• parameters: A p x p matrix of posterior mean partial association estimates. Note that the scale differs between variable types. For continuous variables, the parameter represents partial correlations, for discrete variables partial associations. Edge weights from different variable types are therefore not directly comparable.

• inc_probs: A p x p matrix of posterior inclusion probabilities.

• inc_BF: A p x p matrix of posterior inclusion Bayes factors.

• structure: A p x p adjacency matrix of the median probability model (edges with posterior inclusion probability > 0.5).

• model: A string indicating the model type (e.g., "continuous", "ordinal", "mixed").

• thresholds: Threshold/intercept parameters (bgms only). The format depends on the model type: a matrix for ordinal/binary models, NULL for continuous models, or a list for mixed models. For Blume-Capel variables the two columns are the linear and quadratic effects rather than category thresholds; they are named accordingly, and are also reported in blume_capel_parameters (see below). Where Blume-Capel and ordinal variables share one matrix, the column headers cannot describe both, so the per-row meaning is recorded in the "variable_type" attribute of the matrix.

Returned for bgms and BDgraph:

• structure_probabilities: Posterior probabilities of all visited graph structures (values between 0 and 1).

• graph_weights: Number of times each graph structure was visited.

• sample_graphs: Identifiers for each visited graph structure.

Returned for bgms only:

• convergence_parameter: The Gelman-Rubin (R-hat) convergence statistic for each edge weight parameter. Values close to 1 indicate good convergence.

• MCSE_BF: A matrix with the 95 percent Monte Carlo confidence interval for each inclusion Bayes factor, derived from the Monte Carlo standard error of the Rao-Blackwellized inclusion probability. Entries are NA where the interval is not defined, which happens when the posterior inclusion probability is numerically 0 or 1 and the Bayes factor is therefore 0 or infinite. This is routine for decisive edges rather than a sign of a problem.

Returned when edge_prior = "Stochastic-Block" (bgms only):

• sbm: A list containing Stochastic Block Model results, including posterior_num_blocks (posterior probabilities for each number of clusters), posterior_mean_allocations (posterior mean cluster assignments), posterior_mode_allocations (posterior mode cluster assignments), and posterior_mean_coclustering_matrix (a p x p matrix of pairwise co-clustering proportions).

Interpretable parameter scales (bgms only):

In addition to the raw pairwise interaction parameters in parameters, the following transformations are provided when the model type supports them. They are NULL otherwise.

• partial_correlations: A matrix of posterior mean partial correlations. Available for continuous (GGM) models (full p x p matrix) and for the continuous block of mixed models. NULL for ordinal models.

• precision_matrix: The posterior mean precision (inverse covariance) matrix. Same availability as partial correlations.

• log_odds: A matrix of posterior mean log adjacent-category odds ratios. Available for ordinal/binary models (full p x p matrix) and for the discrete block of mixed models. NULL for continuous models.

Returned for Blume-Capel variables (bgms >= 0.2.0.0):

• blume_capel_parameters: A data frame with two rows per Blume-Capel variable, holding the posterior mean, posterior standard deviation, 95 percent credible interval and R-hat convergence statistic of its linear and quadratic effects, together with the baseline category used. Unlike the category thresholds of an ordinal variable, these are usually of substantive interest: for a variable with baseline category b, the threshold of category x is \mu(x) = \alpha x + \beta (x - b)^2, where \alpha is the linear and \beta the quadratic effect. A negative quadratic effect indicates responses concentrated around the baseline category, a positive one a preference for the extreme categories. Baseline categories are reported on the scale of the input data. This element is NULL when no variable is Blume-Capel, and is not available with bgms 0.1.6.3.

Returned when save = TRUE:

• samples_posterior: A k x iter matrix of posterior samples for each edge weight parameter (k = p*(p-1)/2 edges).

• samples_blume_capel: Posterior samples of the Blume-Capel linear and quadratic effects, with one column per parameter, pooled across chains. Only present when at least one variable is Blume-Capel.

Returned when centrality = TRUE:

• centrality: An iter x p matrix of centrality values for each node at each iteration.

Examples

library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)[1:50, 1:3]

# --- Continuous data (fitted by bgms >= 0.2.0.0, otherwise by BGGM) ---
fit <- easybgm(data, type = "continuous",
                iter = 100,   # for demonstration only; increase for real analyses
                # arguments from bgms to reduce the runtime of the example
                warmup = 50, chain = 2, cores = 1, precision_graph_prior = "joint"   
                )
summary(fit)

## Not run: 
# --- Mixed data using per-variable type vector (requires bgms >= 0.2.0.0) ---
if (utils::packageVersion("bgms") >= "0.2.0.0") {
  dat3 <- data[, 1:3]
  fit_vec <- easybgm(dat3,
                      type = c("ordinal", "ordinal", "continuous"),
                      iter = 100)
}

# --- Extract posterior samples and centrality ---
fit_full <- easybgm(data, type = "continuous",
                     iter = 100, 
                     centrality = TRUE, save = TRUE)

# --- Using BDgraph for continuous data ---
fit_bd <- easybgm(data, type = "continuous",
                   package = "BDgraph",
                   iter = 100)

# --- Using BGGM for continuous data ---
fit_bggm <- easybgm(data, type = "continuous",
                     package = "BGGM",
                     iter = 100)
                   

## End(Not run)

Compare networks across groups using Bayesian inference

Description

Easy comparison of networks using Bayesian inference to extract differences in conditional (in)dependence relations across groups.

Usage

easybgm_compare(
  data,
  type,
  package = NULL,
  not_cont = NULL,
  group_indicator = NULL,
  iter = 1000,
  save = TRUE,
  progress = TRUE,
  ...
)

Arguments

Details

Data types and package support for group comparison

Prior specification

Users may wish to adjust priors via the ... argument. We summarize the bgms options here and refer to bgmCompare and explore for full details.

bgms (>= 0.2.0.0)

• interaction_prior: Prior on the baseline pairwise interactions. Use normal_prior(scale) (default normal_prior(scale = 1)), cauchy_prior(scale), or beta_prime_prior(alpha, beta). For example, a cauchy prior with scale 1 would be specified with adding the argument threshold_prior = cauchy_prior(1) to the easybgm call.

• threshold_prior: Prior on threshold parameters. Default beta_prime_prior(0.5, 0.5), for example, specified by adding threshold_prior = beta_prime_prior(0.5, 0.5) to the easybgm call.

• difference_prior: Indicator prior on group differences. Use bernoulli_prior(inclusion_probability) (default bernoulli_prior(0.5)) or beta_bernoulli_prior(alpha, beta). For example, a beta bernoulli prior with alpha 1 and beta 3 can be specified by adding difference_prior = beta_bernoulli_prior(1, 3) to the easybgm call.

• difference_family: The family of the prior on the magnitude of the pairwise differences, either "Normal" (the default) or "Cauchy". Versions of bgms before 0.2.0.0 had no such argument and always used a Cauchy, so comparison Bayes factors obtained with those versions correspond to difference_family = "Cauchy".

• difference_scale: Scale of the prior on the magnitude of pairwise differences, on the family set by difference_family. Default 1, for example, specified by adding the argument difference_scale = 1 to the easybgm call.

• difference_selection: Logical, whether to perform Bayesian selection on group differences. Default TRUE.

For backwards compatibility of bgms (< 0.2.0.0), the previous prior specifications are still accepted and translated into the relevant constructs. Check the previous bgms version for its prior arguments.

We always encourage researchers to conduct prior sensitivity checks.

Value

An object of class easybgm_compare with the following elements:

Always returned:

• parameters: A p x p matrix of posterior mean differences in partial associations across groups.

• inc_probs: A p x p matrix of posterior inclusion probabilities for group differences (i.e., the probability that an edge differs between groups).

• inc_BF: A p x p matrix of inclusion Bayes factors for group differences.

• structure: A p x p adjacency matrix of the median probability model for differences (edges with posterior inclusion probability > 0.5).

• model: A string indicating the data type used.

Returned for bgms only:

• structure_probabilities: Posterior probabilities of all visited graph structures.

• graph_weights: Number of times each structure was visited.

• sample_graph: Identifiers for each visited structure.

• convergence_parameter: The Gelman-Rubin (R-hat) convergence statistic for each difference parameter. Values close to 1 indicate good convergence.

Returned when save = TRUE:

• samples_posterior: A k x iter matrix of posterior samples for each difference parameter (k = p*(p-1)/2 edges).

Examples

## Not run: 
library(easybgm)
library(bgms)

data <- na.omit(ADHD)

# --- Two-group comparison (list input) ---
group1 <- data[1:10, 1:3]
group2 <- data[11:20, 1:3]

fit <- easybgm_compare(list(group1, group2),
                type = "binary", save = TRUE,
                iter = 100   # for demonstration only
                )
summary(fit)

# --- Multi-group comparison (single dataframe + group_indicator) ---
fit_multi <- easybgm_compare(data[1:80, 1:5],
                group_indicator = rep(c(1, 2, 3, 4), each = 20),
                type = "binary", save = TRUE,
                iter = 100   # for demonstration only
                )
summary(fit_multi)

## End(Not run)

Edge evidence plot

Description

The edge evidence plot colors edges according to their hypothesis testing results: blue for included, dashed + light blue for weakly included, dashed + gray for inconclusive, dashed + light yellow for weakly excluded, and yellow for excluded. This plot can be used to visualize the hypothesis testing results whether edge presence or absence. The edge evidence plot can aid researchers in deciding which edges provide robust inferential conclusions.

Usage

plot_edgeevidence(
  output,
  evidence_thresh = NULL,
  evidence_thresh_strong = 10,
  evidence_thresh_weak = 3,
  edge_legend = TRUE,
  split = FALSE,
  show = "all",
  ...
)

Arguments

Value

Returns a plot

Examples

## Not run: 
library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)[1:50, 1:5]
fit <- easybgm(data, type = "continuous",
                iter = 100   # for demonstration only
                )

plot_edgeevidence(fit)

oldpar <- par(mfrow = c(1,1))

par(mfrow = c(1, 2))
plot_edgeevidence(fit, split = TRUE)

#' par(mfrow = c(1, 3))
plot_edgeevidence(fit, show = "included")
plot_edgeevidence(fit, show = "inconclusive")
plot_edgeevidence(fit, show = "excluded")

par(oldpar)

## End(Not run)

Network plot

Description

The network plot visualizes the strength of interactions between two nodes, the partial associations. Solely edges with a posterior inclusion probability larger than the exc_prob argument (default = 0.5) are shown. Edge thickness and saturation represent the strength of the association; the thicker the edge, the stronger the association. Red edges indicate negative relations and blue edges indicate positive associations.

Usage

plot_network(
  output,
  exc_prob = 0.5,
  evidence_thresh = NULL,
  evidence_thresh_strong = 10,
  dashed = FALSE,
  partial_correlations = FALSE,
  ...
)

Arguments

Value

Returns a plot

Examples

## Not run: 
library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)[1:50, 1:5]
fit <- easybgm(data, type = "continuous",
                iter = 100   # for demonstration only
                )

plot_network(fit)

# Shows all edges with an inclusion probability larger than 0.1
plot_network(fit, exc_prob = 0.1)

# Indicate which edges have insufficient evidence for inclusion through a dashed line
plot_network(fit, dashed = TRUE, evidence_thresh_strong = 10)

## End(Not run)

Print method for easybgm objects

Description

Used to print easybgm results. The nicest overview is created by first feeding it to summary()

Usage

## S3 method for class 'easybgm'
print(x, ...)

Arguments

Value

Prints the output of a Bayesian cross-sectional network model fitted with 'easybgm'

Print method for easybgm_compare objects

Description

Used to print easybgm results. The nicest overview is created by first feeding it to summary()

Usage

## S3 method for class 'easybgm_compare'
print(x, ...)

Arguments

Value

Prints the output of a Bayesian cross-sectional network comparison fitted with 'easybgm'

Plot sensitivity to edge inclusion prior setting

Description

For a given list of easybgm outputs with different prior edge inclusion probabilities, the function plots the percentage of edges that are included, excluded, and inconclusive.

Usage

plot_prior_sensitivity(
  output,
  evidence_thresh_strong = 10,
  evidence_thresh_weak = 3,
  ...
)

Arguments

Details

Prior sensitivity plot

Value

Returns a plot

Examples

## Not run: 
library(easybgm)
library(bgms)

#data <- na.omit(Wenchuan)
#fit1 <- easybgm(data[1:50, 1:5], type = "ordinal",
#               iter = 100,  # for demonstration only
#               inclusion_probability = .1
#               )
#fit2 <- easybgm(data[1:50, 1:5], type = "ordinal",
#                  iter = 100,
#                  inclusion_probability = .5
#             )
#fit3 <- easybgm(data[1:50, 1:5], type = "ordinal",
#                iter = 100, inclusion_probability = .9)

#plot_prior_sensitivity(list(fit1, fit2, fit3))

## End(Not run)

Structure plot

Description

The plot shows the resulting graph structure, i.e. all edges with some evidence of inclusion (i.e., inclusion Bayes factor greater than 1).

Usage

plot_structure(output, ...)

Arguments

Value

Returns a plot

Examples

## Not run: 

library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)
fit <- easybgm(data[1:50, 1:5], type = "ordinal",
                iter = 100   # for demonstration only
               )

plot_structure(fit)

## End(Not run)

Plot Posterior Structure Probabilities

Description

Plots the posterior structure probabilities of all visited structures, sorted from the most to the least probable.

Usage

plot_structure_probabilities(output, as_BF = FALSE, ...)

Arguments

Value

Returns a plot

Examples

## Not run: 

library(easybgm)
library(bgms)

data <- na.omit(Wenchuan)[1:50, 1:5]
fit <- easybgm(data, type = "ordinal", save = TRUE, edge_selection = TRUE,
                iter = 100   # for demonstration only
                )

plot_structure_probabilities(fit)

## End(Not run)

Summary method for easybgm objects

Description

Used to create a object of easybgm results and in turn print it

Usage

## S3 method for class 'easybgm'
summary(
  object,
  evidence_thresh = NULL,
  evidence_thresh_weak = 3,
  evidence_thresh_strong = 10,
  BF_uncertainty = FALSE,
  ...
)

Arguments

Value

Creates and prints the output of a Bayesian cross-sectional network analysis. The summary output has four parts. The first part lists the package used, the number of variables, and the data type. The second part is a matrix of edge-specific information. Each edge is listed in a row. This row contains the posterior parameter estimate, the posterior inclusion probability, the inclusion Bayes factor, and the categorization of the edge. The category encodes whether an edge is included, excluded, or inconclusive based on the inclusion Bayes factor. Users can set the threshold for the Bayes factor classification with the evidence threshold. By default, the threshold is set to 10. The third part of the summary provides aggregated edge information. It lists the number of included, excluded, and inconclusive edges in the network, as well as the number of possible edges. This gives the user a quick overview of the robustness and density of the network. The higher the number of conclusive edges (i.e., classified as either included or excluded), the more robust the network. Conversely, if the network has a high percentage of inconclusive edges, the network is not robust. Researchers should refrain from making strong inferential conclusions. The final output section is a description of the structure uncertainty. It shows the number of structures visited, the number of possible structures, and the highest posterior structure probability. This last section can only be obtained for networks fitted with 'BDgraph' and 'bgms'.

Summary method for easybgm_compare objects

Description

Used to create a object of easybgm results and in turn print it

Usage

## S3 method for class 'easybgm_compare'
summary(
  object,
  evidence_thresh = NULL,
  evidence_thresh_weak = 3,
  evidence_thresh_strong = 10,
  ...
)

Arguments

Value

Creates and prints the output of a Bayesian cross-sectional network analysis. The summary output has four parts. The first part lists the package used, the number of variables, and the data type. The second part is a matrix of edge-specific information. Each edge is listed in a row. This row contains the posterior parameter estimate, the posterior inclusion probability, the inclusion Bayes factor, and the categorization of the edge. The category encodes whether an edge is included, excluded, or inconclusive based on the inclusion Bayes factor. Users can set the threshold for the Bayes factor classification with the evidence threshold. By default, the threshold is set to 10. The third part of the summary provides aggregated edge information. It lists the number of included, excluded, and inconclusive edges in the network, as well as the number of possible edges. This gives the user a quick overview of the robustness and density of the network. The higher the number of conclusive edges (i.e., classified as either included or excluded), the more robust the network. Conversely, if the network has a high percentage of inconclusive edges, the network is not robust. Researchers should refrain from making strong inferential conclusions. The final output section is a description of the structure uncertainty. It shows the number of structures visited, the number of possible structures, and the highest posterior structure probability. This last section can only be obtained for networks fitted with 'BDgraph' and 'bgms'.