Plot Multi-Cluster Multi-Layer Network

Produces a two-layer hierarchical visualization of a clustered network. The bottom layer shows every node arranged inside elliptical cluster shells with full within-cluster and between-cluster edges drawn at the individual-node level. The top layer collapses each cluster into a single summary pie-chart node whose colored slice represents the proportion of within-cluster flow, with edges carrying the aggregated between-cluster weights. Dashed inter-layer lines connect each detail node to its corresponding summary node, making the hierarchical mapping explicit.

Usage

plot_mcml(
  x,
  cluster_list = NULL,
  mode = c("weights", "tna"),
  layer_spacing = NULL,
  spacing = 3,
  shape_size = 1.2,
  summary_size = 4,
  skew_angle = 60,
  aggregation = c("sum", "mean", "max"),
  minimum = 0,
  colors = NULL,
  legend = TRUE,
  show_labels = TRUE,
  nodes = NULL,
  label_size = NULL,
  label_abbrev = NULL,
  node_size = 1.8,
  node_shape = "circle",
  cluster_shape = "circle",
  title = NULL,
  subtitle = NULL,
  title_size = 1.2,
  subtitle_size = 0.9,
  legend_position = "right",
  legend_size = 0.7,
  legend_pt_size = 1.2,
  summary_labels = TRUE,
  summary_label_size = 0.8,
  summary_label_position = 3,
  summary_label_color = "gray20",
  summary_arrows = TRUE,
  summary_arrow_size = 0.1,
  between_arrows = FALSE,
  edge_width_range = c(0.3, 1.3),
  between_edge_width_range = c(0.5, 2),
  summary_edge_width_range = c(0.5, 2),
  edge_alpha = 0.35,
  between_edge_alpha = 0.6,
  summary_edge_alpha = 0.7,
  inter_layer_alpha = 0.5,
  edge_labels = FALSE,
  edge_label_size = 0.5,
  edge_label_color = "gray40",
  edge_label_digits = 2,
  summary_edge_labels = FALSE,
  summary_edge_label_size = 0.6,
  top_layer_scale = c(0.8, 0.25),
  inter_layer_gap = 0.6,
  node_radius_scale = 0.55,
  shell_alpha = 0.15,
  shell_border_width = 2,
  node_border_color = "gray30",
  summary_border_color = "gray20",
  summary_border_width = 2,
  label_color = "gray20",
  label_position = 3,
  ...
)

Arguments

x

A weight matrix, tna object, cograph_network, or cluster_summary object. When a cluster_summary is provided (e.g., from cluster_summary), all aggregation has already been performed and the cluster_list, aggregation, and nodes parameters are ignored. See the Input Formats section for details.

cluster_list

How to assign nodes to clusters. Accepts:

A named list of character vectors — each element contains the node names belonging to that cluster, and the list names become the cluster labels (e.g., list(GroupA = c("A","B"), GroupB = c("C","D"))).
A string giving a column name in the node metadata (from a cograph_network) to use as the grouping variable.
NULL — attempt auto-detection from common column names (cluster, group, etc.) in node metadata.

Ignored when x is a cluster_summary.

mode

What values to display on edges:

"weights": (default) Shows raw aggregated edge values. Useful when absolute magnitudes (e.g., total co-occurrences) matter.
"tna": Row-normalizes the summary matrix so each row sums to 1, producing transition probabilities. Automatically enables edge_labels and summary_edge_labels unless you explicitly set them to FALSE.

layer_spacing

Vertical distance between the bottom and top layers. NULL (default) auto-calculates a gap that prevents overlap based on cluster positions and shell sizes. Increase for more vertical separation; decrease to make the plot more compact.

spacing

Distance from the center to each cluster's position in the bottom layer. Larger values spread clusters farther apart. Default 3.

shape_size

Radius of each cluster's elliptical shell in the bottom layer. Increase when nodes overlap or shells feel cramped. Default 1.2.

summary_size

Size of the pie-chart summary nodes in the top layer. Controls the visual radius of each pie chart. Default 4.

skew_angle

Perspective tilt angle in degrees (0–90). At 0 the bottom layer is viewed from directly above (fully circular); at 90 it collapses to a flat line. Values around 45–70 give a natural table-top perspective. Default 60.

aggregation

Method for collapsing individual edge weights into between-cluster and within-cluster summaries:

"sum": (default) Total flow — appropriate when you care about the volume of all transitions between clusters.
"mean": Average flow per node pair — useful when clusters differ in size and you want a size-normalized comparison.
"max": Strongest single edge — highlights the dominant connection between each pair of clusters.

Ignored when x is a cluster_summary.

minimum

Edge weight threshold. Edges with absolute weight below this value are not drawn. Set to a small positive value (e.g., 0.01) to remove visual noise from near-zero edges. Default 0 (show all).

colors

Character vector of colors for the clusters. The first color is applied to the first cluster, and so on. Must have length equal to the number of clusters, or it will be recycled. When NULL (default), colors are auto-generated from a colorblind-safe palette.

legend

Logical. Whether to draw a legend mapping cluster names to colors. Default TRUE.

show_labels

Logical. Show node labels in the bottom layer. Default TRUE. Set to FALSE for dense networks where labels create clutter.

nodes

Node metadata data frame for custom display labels. Must contain a label column whose values match the row/column names of the weight matrix. If a labels column also exists, those values are used as display text (e.g., full names instead of codes). Display priority: labels column > label column. Ignored when x is a cluster_summary or cograph_network (which carries its own node metadata).

label_size

Text size (cex) for bottom-layer node labels. NULL (default) auto-scales to 0.6. Increase for readability in publication figures; decrease for dense networks.

label_abbrev

Controls label abbreviation to reduce overlap:

NULL — no abbreviation (show full labels).
An integer — truncate labels to this many characters.
"auto" — adaptively abbreviates based on the total number of nodes: more nodes triggers shorter abbreviations.

node_size

Size of individual detail nodes in the bottom layer. This controls the pie-chart radius for each node. Default 1.8.

node_shape

Shape for detail nodes in the bottom layer. Supported values: "circle", "square", "diamond", "triangle". Can be a single value applied to all nodes or a character vector of length equal to the number of nodes (one shape per node). Default "circle".

cluster_shape

Shape for summary nodes in the top layer. Same supported values as node_shape. Can be a single value or a vector of length equal to the number of clusters. Default "circle".

title

Main plot title displayed above the figure. Default NULL (no title).

subtitle

Subtitle displayed below the title. Default NULL (no subtitle).

title_size

Text size (cex.main) for the title. Default 1.2.

subtitle_size

Text size (cex.sub) for the subtitle. Default 0.9.

legend_position

Where to place the legend: "right", "left", "top", "bottom", or "none" to suppress it entirely. Default "right".

legend_size

Text size (cex) for legend labels. Default 0.7.

legend_pt_size

Point size (pt.cex) for legend symbols. Default 1.2.

summary_labels

Logical. Show cluster name labels next to the summary pie-chart nodes in the top layer. Default TRUE.

summary_label_size

Text size for summary labels. Default 0.8.

summary_label_position

Position of summary labels relative to nodes: 1 = below, 2 = left, 3 = above, 4 = right. Default 3 (above).

summary_label_color

Color for summary labels. Default "gray20".

summary_arrows

Logical. Draw arrowheads on summary-layer directed edges. Set to FALSE for undirected networks. Default TRUE.

summary_arrow_size

Size of arrowheads on summary edges. Default 0.10.

between_arrows

Logical. Draw arrowheads on between-cluster edges in the bottom layer. Default FALSE.

edge_width_range

Numeric vector c(min, max) controlling the line-width range for within-cluster edges in the bottom layer. The weakest edge gets min and the strongest gets max. Default c(0.3, 1.3).

between_edge_width_range

Numeric vector c(min, max) for between-cluster edges in the bottom layer (shell-to-shell lines). Default c(0.5, 2.0).

summary_edge_width_range

Numeric vector c(min, max) for summary edges in the top layer. Default c(0.5, 2.0).

edge_alpha

Transparency (0–1) for within-cluster edges. Lower values make these edges more subtle, keeping focus on between-cluster structure. Default 0.35.

between_edge_alpha

Transparency (0–1) for between-cluster edges in the bottom layer. Default 0.6.

summary_edge_alpha

Transparency (0–1) for summary-layer edges. Default 0.7.

inter_layer_alpha

Transparency (0–1) for the dashed inter-layer lines connecting detail nodes to their summary node. Lower values make these scaffolding lines less visually dominant. Default 0.5.

edge_labels

Logical. Show numeric weight labels on within-cluster edges. Default FALSE (automatically set to TRUE when mode = "tna").

edge_label_size

Text size for within-cluster edge labels. Default 0.5.

edge_label_color

Color for within-cluster edge labels. Default "gray40".

edge_label_digits

Number of decimal places for edge weight labels on both layers. Default 2.

summary_edge_labels

Logical. Show numeric weight labels on summary-layer edges. Default FALSE (automatically set to TRUE when mode = "tna").

summary_edge_label_size

Text size for summary edge labels. Default 0.6.

top_layer_scale

Numeric vector c(x_scale, y_scale) controlling the horizontal and vertical radii of the oval on which summary nodes are placed, as multiples of spacing. Widen with c(1.0, 0.25) or flatten with c(0.8, 0.15) to adjust the top-layer shape. Default c(0.8, 0.25).

inter_layer_gap

Vertical gap between the top of the bottom layer and the bottom of the top layer, as a multiple of spacing. Increase to separate the layers more. Default 0.6.

node_radius_scale

Radius of the circle on which nodes are arranged inside each cluster shell, as a fraction of shape_size. Increase to push nodes outward toward the shell border; decrease to pack them tighter. Default 0.55.

shell_alpha

Fill transparency (0–1) for cluster shells. Higher values make shells more opaque, giving stronger visual grouping but potentially obscuring edges. Default 0.15.

shell_border_width

Line width for cluster shell borders. Default 2.

node_border_color

Border color for detail nodes in the bottom layer. Default "gray30".

summary_border_color

Border color for summary pie-chart nodes. Default "gray20".

summary_border_width

Border line width for summary nodes. Default 2.

label_color

Text color for detail node labels. Default "gray20".

label_position

Position of detail node labels: 1 = below, 2 = left, 3 = above, 4 = right. Default 3.

...

Additional arguments (currently unused).

Value

Invisibly returns the cluster_summary object used for plotting. This object can be passed back to plot_mcml() to avoid recomputation, inspected with print(), or fed to as_tna for further analysis.

Details

Use plot_mcml when you need a simultaneous micro/macro view of cluster structure — the bottom layer reveals internal cluster dynamics while the top layer provides a bird's-eye summary. For a flat multi-cluster plot without the summary layer, see plot_mtna. For stacked multilevel/multiplex layers, see plot_mlna.

Two workflows:

Direct: pass a weight matrix (or tna / cograph_network object) together with cluster_list. The function calls cluster_summary internally to compute aggregated weights.
Pre-computed: call cluster_summary yourself, inspect or modify the result, then pass the cluster_summary object as x. This avoids redundant computation when you plot the same clustering repeatedly with different visual settings.

Mode:

"weights" (default) — displays raw aggregated edge values. Use this when the absolute magnitude of transitions matters.
"tna" — row-normalizes the summary matrix to transition probabilities (rows sum to 1) and automatically enables edge labels on both layers (unless you explicitly set edge_labels or summary_edge_labels to FALSE).

Layout logic: Bottom-layer clusters are arranged on a circle of radius spacing, flattened by the perspective skew_angle. Nodes inside each cluster sit on a smaller circle of radius shape_size * node_radius_scale. The top-layer summary nodes are placed on an oval above the bottom layer whose proportions are controlled by top_layer_scale.

Input Formats

x accepts four types:

matrix: A square numeric weight matrix with row/column names matching the node identifiers in cluster_list.
tna: A TNA model object. The $weights matrix is extracted automatically.
cograph_network: A cograph network object. Weights are extracted via to_matrix() and node metadata (display labels) is read from the $nodes data frame.
cluster_summary: A pre-computed summary from cluster_summary. When this type is passed, the cluster_list, aggregation, and nodes parameters are ignored because the summary already contains everything needed.

Edge Types

The plot contains four distinct edge categories, each with its own set of visual parameters:

Within-cluster (bottom): Edges connecting nodes inside the same cluster shell. Controlled by edge_width_range, edge_alpha, edge_labels, edge_label_size, edge_label_color, and edge_label_digits.
Between-cluster (bottom): Edges from one cluster shell to another, drawn between shell borders. Controlled by between_edge_width_range and between_edge_alpha.
Summary (top): Edges between summary pie-chart nodes in the top layer. Controlled by summary_edge_width_range, summary_edge_alpha, summary_edge_labels, summary_edge_label_size, summary_arrows, and summary_arrow_size.
Inter-layer (dashed): Dashed lines connecting each detail node to its cluster's summary node. Controlled by inter_layer_alpha.

Customization Quick Reference

Visual element	Key parameters
Cluster spacing / perspective	`spacing`, `skew_angle`
Cluster shell appearance	`shape_size`, `shell_alpha`, `shell_border_width`, `colors`
Detail nodes	`node_size`, `node_shape`, `node_border_color`
Detail labels	`show_labels`, `label_size`, `label_abbrev`, `label_color`, `label_position`
Summary nodes	`summary_size`, `cluster_shape`, `summary_border_color`, `summary_border_width`
Summary labels	`summary_labels`, `summary_label_size`, `summary_label_color`, `summary_label_position`
Within-cluster edges	`edge_width_range`, `edge_alpha`, `edge_labels`
Between-cluster edges	`between_edge_width_range`, `between_edge_alpha`
Summary edges	`summary_edge_width_range`, `summary_edge_alpha`, `summary_edge_labels`, `summary_arrows`
Inter-layer lines	`inter_layer_alpha`
Top-layer layout	`top_layer_scale`, `inter_layer_gap`
Title / legend	`title`, `subtitle`, `legend`, `legend_position`

Examples

# --- Setup: create a test matrix ---
mat <- matrix(runif(36), 6, 6)
diag(mat) <- 0
colnames(mat) <- rownames(mat) <- LETTERS[1:6]

clusters <- list(
  Cluster1 = c("A", "B"),
  Cluster2 = c("C", "D"),
  Cluster3 = c("E", "F")
)

# 1. Basic usage — pass matrix + clusters directly
plot_mcml(mat, clusters)


# 2. Pre-compute with cluster_summary for reuse
cs <- cluster_summary(mat, clusters)
plot_mcml(cs)


if (FALSE) { # \dontrun{
# 3. TNA mode — transition probabilities with edge labels
plot_mcml(mat, clusters, mode = "tna")

# 4. Custom shapes — different shape per cluster
plot_mcml(mat, clusters,
  node_shape = "diamond",
  cluster_shape = c("circle", "square", "triangle")
)

# 5. Styling — custom colors, transparency, edge widths
plot_mcml(mat, clusters,
  colors = c("#1b9e77", "#d95f02", "#7570b3"),
  edge_alpha = 0.5,
  between_edge_alpha = 0.8,
  shell_alpha = 0.25,
  edge_width_range = c(0.5, 2.0)
)

# 6. Edge labels on both layers
plot_mcml(mat, clusters,
  edge_labels = TRUE,
  summary_edge_labels = TRUE,
  edge_label_digits = 1
)

# 7. Layout tuning — adjust spacing, perspective, and layer gap
plot_mcml(mat, clusters,
  spacing = 4,
  skew_angle = 45,
  top_layer_scale = c(1.0, 0.3),
  inter_layer_gap = 0.8
)

# 8. With mean aggregation for size-normalized comparison
plot_mcml(mat, clusters,
  aggregation = "mean",
  title = "Mean-aggregated cluster network"
)

# 9. Label abbreviation for dense networks
big_mat <- matrix(runif(400), 20, 20)
diag(big_mat) <- 0
colnames(big_mat) <- rownames(big_mat) <- paste0("Node_", 1:20)
big_clusters <- list(
  Alpha = paste0("Node_", 1:7),
  Beta  = paste0("Node_", 8:14),
  Gamma = paste0("Node_", 15:20)
)
plot_mcml(big_mat, big_clusters, label_abbrev = "auto")

# 10. Minimal clean plot — no legend, no labels, no arrows
plot_mcml(mat, clusters,
  legend = FALSE,
  show_labels = FALSE,
  summary_labels = FALSE,
  summary_arrows = FALSE
)
} # }