Package {dynamicmultiplex}

Animate multiplex networks as a GIF by layer

Description

Creates one frame per layer and colors nodes by community using colorblind-friendly ColorBrewer palettes (Set2 or Dark2).

Usage

animate_multilayer_gif(
  layers,
  fit = NULL,
  community_memberships = NULL,
  output_file,
  directed = FALSE,
  fps = 2,
  width = 800,
  height = 600,
  layout = "layout_with_fr",
  palette = "Dark2"
)

Arguments

Value

The path to the created GIF.

Examples

if (requireNamespace("ggplot2", quietly = TRUE) &&
    requireNamespace("gganimate", quietly = TRUE) &&
    requireNamespace("gifski", quietly = TRUE)) {
  set.seed(123)
  layers <- lapply(1:3, function(i) {
    m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
    m <- pmax(m, t(m))
    diag(m) <- 0
    m
  })
  fit <- fit_multilayer_jaccard(layers, algorithm = "louvain")
  gif_path <- animate_multilayer_gif(
    layers,
    fit = fit,
    output_file = tempfile(fileext = ".gif"),
    fps = 2,
    width = 200,
    height = 150
  )
}

Bootstrap confidence intervals for multilayer community detection

Description

Quantifies the uncertainty of multilayer community detection by refitting communities on n_boot resampled networks, using a parametric network bootstrap: within- and between-community edge probabilities (and, for weighted networks, edge-weight pools) are estimated from the observed network using the point-estimate partition, and each replicate redraws the full edge set from those estimates. This reproduces the variability of fresh data, including which edges exist.

Uncertainty is quantified on the cross-layer meta-communities (the tracked partition from the second-stage detection), not the independently-detected per-layer communities. Co-assignment therefore answers "do these two nodes belong to the same persistent community," and the community count is the number of meta-communities per layer.

Versions before 1.1.0 instead used a Bayesian bootstrap on edge weights (Exponential(1) multipliers on a fixed topology). That scheme was removed: because it never varies which edges exist, it understates the variability of fresh data, and in simulation studies confidence intervals built from it undercovered substantially (pairwise co-assignment intervals covered ~45-48 percent at a nominal 95 percent).

Usage

bootstrap_multilayer(
  layers,
  fit_type = c("jaccard", "overlap", "weighted_jaccard", "weighted_overlap", "identity"),
  algorithm = c("louvain", "leiden"),
  n_boot = 100,
  layer_links = NULL,
  min_similarity = 0,
  resolution_parameter = 1,
  directed = FALSE,
  seed = NULL,
  objective = NULL
)

Arguments

Value

A list of class "multilayer_bootstrap" with components:

n_boot

Number of completed bootstrap replicates.

co_assignment

Per-layer co-assignment probability matrices on the meta-communities (probability two nodes share a persistent community).

node_stability

Per-layer vectors giving the fraction of replicates in which each node was assigned to its modal community.

modularity_samples

Per-layer vectors of bootstrap modularity values.

community_count_reproducibility

Per-layer numeric vector: the share of completed replicates whose meta-community count equals the observed-network count. A descriptive stability measure. The raw per-replicate community counts are intentionally not returned.

point_estimate

The fit result from the original data.

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
boot <- bootstrap_multilayer(
  layers,
  fit_type = "jaccard",
  algorithm = "louvain",
  n_boot = 5,
  seed = 123
)
names(boot)

Wilson confidence intervals for node-pair co-assignment

Description

For every pair of nodes in every layer, computes a Wilson score interval for the co-clustering propensity: the probability that the fitted community detection procedure places the two nodes in the same community when the data are perturbed. The point estimate is the co-assignment probability from bootstrap_multilayer (the share of bootstrap replicates in which the pair was co-assigned), and the interval treats the n_boot replicates as binomial draws.

Because co-assignment is label-invariant (it never compares community labels across replicates, only whether two nodes sit together), it avoids the label-switching problem that makes per-node membership intervals ill-defined.

Usage

co_assignment_ci(boot_result, alpha = 0.05)

Arguments

Value

A list with one element per layer. Each element is a list with components:

estimate

n x n matrix of co-assignment probabilities.

lower

n x n matrix of Wilson lower bounds.

upper

n x n matrix of Wilson upper bounds.

Diagonals are 1 by construction.

Warning

These intervals quantify the stability of the detection procedure, not the probability that two nodes truly share a community. The Wilson interval is exact for the binomial sampling of bootstrap replicates; its coverage of the fresh-data co-clustering propensity was evaluated in the package's simulation study (see the package NEWS for the release in which validation results were incorporated). Interpret cautiously on networks with fewer than 100 nodes, where community detection itself is unstable.

See Also

community_est for community-count point estimates and node stability summaries.

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
boot <- bootstrap_multilayer(
  layers,
  fit_type = "jaccard",
  algorithm = "louvain",
  n_boot = 5,
  seed = 123
)
pci <- co_assignment_ci(boot, alpha = 0.05)
pci[[1]]$estimate[1:4, 1:4]
pci[[1]]$lower[1:4, 1:4]

Summarize bootstrap community-count reproducibility (meta-communities)

Description

Reports, for each layer, the community count from the observed network together with its bootstrap reproducibility: the proportion of bootstrap replicates in which the fitted number of communities equals the observed-network count. It also returns mean node stability, per-node stability, and the co-assignment matrices.

Usage

community_est(boot_result)

Arguments

Value

A list with components:

community_count

Data frame with columns layer, estimate (the observed-network meta-community count), and reproducibility (share of bootstrap replicates whose community count equals estimate, in [0, 1]).

report

Character vector, one plain-language sentence per layer.

mean_node_stability

Data frame with columns layer, mean_stability.

node_stability

Per-layer stability vectors.

co_assignment

Per-layer co-assignment matrices.

Why this is not a confidence interval

Earlier versions returned a percentile community_count_ci. It was replaced in version 1.1.0 with a reproducibility summary because the interval's coverage is not robust to model misspecification. In a large simulation study the nominal 95 percent community-count interval covered the truth at or above the nominal level on well-specified planted-partition networks (about 0.99 for n >= 100 nodes), but coverage collapsed to about 0.62 when community sizes were strongly skewed, and no observable diagnostic reliably separated the trustworthy cases from the rest. Rather than ship an interval that silently undercovers, the function now reports how often the community count reproduces under resampling. This is a descriptive stability measure, not a calibrated interval: it makes no claim about the probability that any range contains the true community count. For a validated interval, use co_assignment_ci, whose node-pair coverage held across the same misspecification stress tests. The raw per-replicate community counts are intentionally not exposed anywhere in the package output; only this reproducibility summary is returned.

See Also

co_assignment_ci for calibrated node-pair co-assignment intervals.

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
boot <- bootstrap_multilayer(
  layers,
  fit_type = "jaccard",
  algorithm = "louvain",
  n_boot = 5,
  seed = 123
)
est <- community_est(boot)
est$community_count
est$report

Extract cross-layer meta-community membership

Description

Returns the tracked (cross-layer) community assignment produced by the second-stage detection: for each layer, a vector giving every node's meta-community. Unlike the per-layer layer_communities (detected independently, ignoring the coupling), the meta-communities are the partition that reflects the interlayer ties and any custom layer_links. This is the membership that bootstrap_multilayer validates.

Usage

extract_meta_membership(fit)

Arguments

Value

A list with one integer vector per layer giving each node's meta-community assignment (node order).

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m)); diag(m) <- 0; m
})
fit <- fit_multilayer_jaccard(layers, algorithm = "leiden")
extract_meta_membership(fit)

Fit multilayer communities with Hungarian snapshot matching

Description

Detects communities independently in each layer and then tracks them across time by matching community labels between consecutive layers with the Hungarian (optimal linear-sum assignment) algorithm applied to the community overlap (contingency) matrix. This is a two-stage snapshot-and-match tracker: unlike the coupling-based fits (fit_multilayer_jaccard, fit_multilayer_overlap, fit_multilayer_identity_ties), communities are found per layer and aligned post hoc, not jointly optimised on a coupled supra-graph. It provides the common "independent detection + optimal label matching" baseline (e.g. per-layer Leiden matched with the Hungarian algorithm) as a first-class method with the same interface as the other fits.

Usage

fit_multilayer_hungarian(
  layers,
  algorithm = c("louvain", "leiden"),
  resolution_parameter = 1,
  directed = FALSE,
  objective = NULL,
  seed = NULL
)

Arguments

Details

Matching is sequential: layer t is aligned to layer t-1. For each adjacent pair the community overlap matrix is completed to a square cost matrix and solve_LSAP maximises total overlap; unmatched current communities receive fresh labels. The result is a consistently-labelled sequence suitable for extract_meta_membership, bootstrap_multilayer, and the plotting helpers.

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities), detected independently.

meta_communities

The tracked partition: one integer vector per layer where labels are aligned across consecutive layers by Hungarian matching on community overlap. A community with no positive-overlap match is given a new label (a birth); labels not carried forward are treated as deaths. See extract_meta_membership.

interlayer_ties

NULL - no coupled supra-graph is built.

method

"hungarian".

layer_links

Sequential adjacent-layer links (the chain the matcher walks).

See Also

fit_multilayer_jaccard, fit_multilayer_overlap, fit_multilayer_identity_ties for coupling-based tracking.

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m)); diag(m) <- 0; m
})
fit <- fit_multilayer_hungarian(layers, algorithm = "leiden")
extract_meta_membership(fit)

Fit multilayer communities with identity interlayer ties

Description

Runs Louvain or Leiden community detection for each layer and creates interlayer ties between the same node in selected adjacent layers. With allow_unequal_nodes = TRUE, layers may contain different node sets; only nodes present in both layers of a linked pair receive interlayer edges. Nodes are matched by V(g)$name when available, or by vertex index otherwise.

For this specification the cross-layer meta_communities are obtained by Mucha (2010) multislice modularity: the layers are stacked into a single supra-graph (intra-layer edges are each layer's own adjacency) with interlayer identity edges joining each node to its copies in the coupled layers (weighted by layer_links), and one community detection is run on the whole supra-graph. The coupling strength is the layer-link weight.

Usage

fit_multilayer_identity_ties(
  layers,
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  resolution_parameter = 1,
  omega = 1,
  directed = FALSE,
  objective = NULL,
  seed = NULL,
  allow_unequal_nodes = FALSE
)

Arguments

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities). Detected independently per layer.

meta_communities

The cross-layer tracked partition from the second-stage detection: one integer vector per layer giving each node's meta-community. This is the membership that reflects the interlayer ties and any custom layer_links, and the one validated by bootstrap_multilayer. See extract_meta_membership.

interlayer_ties

Interlayer similarity edges between communities (plus self-loops).

layer_links

The layer connectivity used.

Directed networks

Directed layers are stored as directed graphs and the interlayer self-loop weighting is directed-aware, but community detection collapses directed layers to weighted undirected graphs on both Louvain and Leiden (igraph's detectors are undirected-only). For detection that respects edge direction, use the Python package with algorithm = "leiden".

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
fit <- fit_multilayer_identity_ties(layers, algorithm = "louvain")
names(fit)

Fit multilayer communities and interlayer weighted Jaccard ties

Description

Runs Louvain or Leiden community detection for each layer and creates interlayer ties between communities in selected layer pairs using weighted Jaccard similarity.

Usage

fit_multilayer_jaccard(
  layers,
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  min_similarity = 0,
  resolution_parameter = 1,
  directed = FALSE,
  add_self_loops = TRUE,
  self_loop_multiplier = 1,
  objective = NULL,
  seed = NULL
)

Arguments

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities). Detected independently per layer.

meta_communities

The cross-layer tracked partition from the second-stage detection: one integer vector per layer giving each node's meta-community. This is the membership that reflects the interlayer ties and any custom layer_links, and the one validated by bootstrap_multilayer. See extract_meta_membership.

interlayer_ties

Interlayer similarity edges between communities (plus self-loops).

layer_links

The layer connectivity used.

Directed networks

Directed layers are stored as directed graphs and the interlayer self-loop weighting is directed-aware, but community detection collapses directed layers to weighted undirected graphs on both Louvain and Leiden (igraph's detectors are undirected-only). For detection that respects edge direction, use the Python package with algorithm = "leiden".

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
fit <- fit_multilayer_jaccard(layers, algorithm = "louvain")
names(fit)
fit$layer_communities[[1]]$membership

Fit multilayer communities and interlayer weighted overlap ties

Description

Runs Louvain or Leiden community detection for each layer and creates interlayer ties between communities in selected layer pairs using a weighted overlap coefficient.

Usage

fit_multilayer_overlap(
  layers,
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  min_similarity = 0,
  resolution_parameter = 1,
  directed = FALSE,
  add_self_loops = TRUE,
  self_loop_multiplier = 1,
  objective = NULL,
  seed = NULL
)

Arguments

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities). Detected independently per layer.

meta_communities

The cross-layer tracked partition from the second-stage detection: one integer vector per layer giving each node's meta-community. This is the membership that reflects the interlayer ties and any custom layer_links, and the one validated by bootstrap_multilayer. See extract_meta_membership.

interlayer_ties

Interlayer similarity edges between communities (plus self-loops).

layer_links

The layer connectivity used.

Directed networks

Directed layers are stored as directed graphs and the interlayer self-loop weighting is directed-aware, but community detection collapses directed layers to weighted undirected graphs on both Louvain and Leiden (igraph's detectors are undirected-only). For detection that respects edge direction, use the Python package with algorithm = "leiden".

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
  m <- pmax(m, t(m))
  diag(m) <- 0
  m
})
fit <- fit_multilayer_overlap(layers, algorithm = "louvain")
names(fit)

Fit multilayer communities and interlayer node-strength weighted Jaccard ties

Description

Runs Louvain or Leiden community detection for each layer and creates interlayer ties between communities in selected layer pairs using node-strength weighted Jaccard similarity.

Usage

fit_multilayer_weighted_jaccard(
  layers,
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  min_similarity = 0,
  resolution_parameter = 1,
  directed = FALSE,
  add_self_loops = TRUE,
  self_loop_multiplier = 1,
  objective = NULL,
  seed = NULL
)

Arguments

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities). Detected independently per layer.

meta_communities

The cross-layer tracked partition from the second-stage detection: one integer vector per layer giving each node's meta-community. This is the membership that reflects the interlayer ties and any custom layer_links, and the one validated by bootstrap_multilayer. See extract_meta_membership.

interlayer_ties

Interlayer similarity edges between communities (plus self-loops).

layer_links

The layer connectivity used.

Directed networks

Directed layers are stored as directed graphs and the interlayer self-loop weighting is directed-aware, but community detection collapses directed layers to weighted undirected graphs on both Louvain and Leiden (igraph's detectors are undirected-only). For detection that respects edge direction, use the Python package with algorithm = "leiden".

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  w <- matrix(runif(64), 8, 8) * matrix(rbinom(64, 1, 0.35), 8, 8)
  w <- (w + t(w)) / 2
  diag(w) <- 0
  w
})
fit <- fit_multilayer_weighted_jaccard(layers, algorithm = "louvain")
names(fit)

Fit multilayer communities and interlayer node-strength weighted overlap ties

Description

Runs Louvain or Leiden community detection for each layer and creates interlayer ties between communities in selected layer pairs using node-strength weighted overlap coefficient.

Usage

fit_multilayer_weighted_overlap(
  layers,
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  min_similarity = 0,
  resolution_parameter = 1,
  directed = FALSE,
  add_self_loops = TRUE,
  self_loop_multiplier = 1,
  objective = NULL,
  seed = NULL
)

Arguments

Value

A list of class "multilayer_community_fit" with components:

layer_communities

Per-layer community detection (each with membership and communities). Detected independently per layer.

meta_communities

The cross-layer tracked partition from the second-stage detection: one integer vector per layer giving each node's meta-community. This is the membership that reflects the interlayer ties and any custom layer_links, and the one validated by bootstrap_multilayer. See extract_meta_membership.

interlayer_ties

Interlayer similarity edges between communities (plus self-loops).

layer_links

The layer connectivity used.

Directed networks

Directed layers are stored as directed graphs and the interlayer self-loop weighting is directed-aware, but community detection collapses directed layers to weighted undirected graphs on both Louvain and Leiden (igraph's detectors are undirected-only). For detection that respects edge direction, use the Python package with algorithm = "leiden".

Examples

set.seed(123)
layers <- lapply(1:3, function(i) {
  w <- matrix(runif(64), 8, 8) * matrix(rbinom(64, 1, 0.35), 8, 8)
  w <- (w + t(w)) / 2
  diag(w) <- 0
  w
})
fit <- fit_multilayer_weighted_overlap(layers, algorithm = "louvain")
names(fit)

Plot an alluvial view of community transitions over time

Description

Plot an alluvial view of community transitions over time

Usage

plot_multilayer_alluvial(fit, max_nodes = NULL, palette = "Dark2")

Arguments

Value

A ggplot object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE) &&
    requireNamespace("ggalluvial", quietly = TRUE)) {
  set.seed(123)
  layers <- lapply(1:3, function(i) {
    m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
    m <- pmax(m, t(m))
    diag(m) <- 0
    m
  })
  fit <- fit_multilayer_jaccard(layers, algorithm = "louvain")
  p <- plot_multilayer_alluvial(fit)
}

Plot multiplex networks as wrapped panels

Description

Draws one panel per layer with nodes colored by community assignment, using a faceted/wrapped layout.

Usage

plot_multilayer_series(
  layers,
  fit = NULL,
  community_memberships = NULL,
  directed = FALSE,
  layout = "layout_with_fr",
  ncol = 3,
  palette = "Dark2"
)

Arguments

Value

A ggplot object.

Examples

if (requireNamespace("ggplot2", quietly = TRUE)) {
  set.seed(123)
  layers <- lapply(1:3, function(i) {
    m <- matrix(rbinom(64, 1, 0.35), nrow = 8)
    m <- pmax(m, t(m))
    diag(m) <- 0
    m
  })
  fit <- fit_multilayer_jaccard(layers, algorithm = "louvain")
  p <- plot_multilayer_series(layers, fit = fit)
}

Simulate multiplex layers and fit interlayer models

Description

Generates synthetic multiplex network layers using a planted partition model, then fits one of the provided interlayer tie strategies.

Usage

simulate_and_fit_multilayer(
  n_nodes = 100,
  n_layers = 4,
  n_communities = 4,
  p_in = 0.2,
  p_out = 0.05,
  fit_type = c("jaccard", "overlap", "weighted_jaccard", "weighted_overlap", "identity"),
  algorithm = c("louvain", "leiden"),
  layer_links = NULL,
  min_similarity = 0,
  seed = NULL,
  directed = FALSE
)

Arguments

Value

A list containing simulated layers, true memberships, and fit results.

Examples

sim <- simulate_and_fit_multilayer(
  n_nodes = 30,
  n_layers = 3,
  n_communities = 3,
  fit_type = "jaccard",
  algorithm = "louvain",
  seed = 123
)
names(sim)