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Includes every change listed under 1.3.2 below, which was not
released separately. The same changes are in the Python package
dynamic-multiplex 1.4.0.
The bootstrap is kept only for the stability score s used to
compare two fits of the same network (for example DynMux against
multislice). co_assignment_ci() and
community_est() are removed, and
partition_stability() now returns only
stability, stability_by_layer,
stability_mc_se, metric and
report: the calibrated accuracy floor, node floors,
decided-pair outputs, the decided and
calibration_table arguments and the bundled calibration
table are removed. Their coverage was not reliable.
R fit functions now default to seed = 123, as in the
Python package (previously NULL, the caller’s random number
stream). Pass seed = NULL for unseeded detection. Because
bootstrap refits are now seeded, R values of s differ slightly from
1.3.x (for example 0.916 to 0.921 on a test network, within Monte Carlo
error).
allow_unequal_nodes = TRUE now requires vertex names
on every layer even when layers have the same size, since nodes can
enter and leave without the size changing. Previously same-size unnamed
layers were matched by position. (Python: adjacency matrices are
rejected with allow_unequal_nodes=True.)
repair_chains and repair_min_similarity
(two-stage fit functions, default off). Stage-2 modularity tends to cut
a long-lived community into time segments (a resolution-limit effect on
chains of communities). With repair_chains = TRUE a group
that ends at layer s and one that starts at a linked layer t are joined
when their communities are mutual best matches (Kawadia and Sreenivasan
2012) with similarity at least repair_min_similarity
(default 0.2; Greene et al. 2010 use a matching threshold). Groups that
coexist are never merged. Joins are logged in
chain_repairs.
tracking = "filtered" (two-stage fit functions;
default "smoothed", the previous behaviour). Stage 2 runs
forward in time: the meta ids of layers 1..t depend only on layers 1..t,
so fitted labels carry no information from later layers. Works with
Leiden and Louvain and with repair_chains. Needs a seed
(seed = NULL is an error), because unseeded stage-1 fits of
later layers would shift the random stream that stage 2 uses.
layers_from_membership() builds one weighted layer
per time slice from group memberships (wide 0/1 matrices or long
node-group tables), with weighting = "count",
"size" or "kumar" (Kumar et al. hypergraph
reweighting, as in hypernetx 2.4.3). There is no default weighting, each
slice is built on its own, and rescale = "mean" puts slices
on a common scale for the multislice coupling.
bootstrap_multilayer() gains
allow_unequal_nodes (nodes entering and leaving) and passes
tracking, repair_chains and
repair_min_similarity to the refits. Layers with different
named node sets now stop with an error unless
allow_unequal_nodes = TRUE.
partition_membership_bipartite() partitions membership
slices by Barber’s bipartite modularity (leidenalg’s bipartite
construction, Leiden only); partition_membership_strict()
by strict (all-or-nothing) hypergraph modularity (hypernetx reference
pipeline, optional extra [hypergraph], which needs pandas
< 3); fit_multilayer_from_partitions() tracks supplied
per-slice partitions with the DynMux second stage or Hungarian matching.
They are comparison specifications; in pilot simulations both did worse
than the projections in layers_from_membership().fit_multilayer_identity_ties() (undirected): the
multislice local mover scored staying in a community the vertex has no
tie into as 0, which could refuse an improving move (the same flaw was
fixed for directed slices in 1.3.2). The stay score is now exact.
Results on the package’s regression networks are unchanged.
Python: bootstrap_multilayer() silently paired nodes
by position when networkx layers had the same size but different nodes;
it now stops unless allow_unequal_nodes=True, which matches
nodes by label.
Not released separately; included in 1.4.0.
All fit functions, bootstrap_multilayer() and
simulate_and_fit_multilayer() now default to
algorithm = "leiden" (previously "louvain"),
matching the Python package. Pass algorithm = "louvain" to
reproduce earlier default results.
Input policy (shared with the Python package): within-layer
self-loops and zero-weight edges are dropped for both adjacency-matrix
and igraph input. Previously a loop-bearing
igraph layer kept its loops while the equivalent matrix did
not. Layers with no vertices now stop with a clear error.
fit_multilayer_identity_ties() with
directed = TRUE: the multislice stage built every slice as
undirected, so each arc became an undirected edge and a reciprocated
pair counted twice. A fully reciprocated directed network was therefore
fitted as if omega were halved relative to its undirected
twin, and one-way arcs were symmetrised. Each slice now keeps arc
direction, with Leicht and Newman’s directed null model k_out k_in /
m_s; the interlayer identity ties stay undirected. With
directed = TRUE every layer must be directed (error
otherwise). Directed layers reaching the multislice stage with
directed = FALSE are symmetrised as before, now with a
warning. Results for undirected networks are unchanged
(regression-tested). Same fix in the Python package.
fit_*() with directed igraph layers and
directed = FALSE stopped with an igraph error in per-layer
detection. Such layers are now collapsed to weighted undirected graphs
(reciprocal arc weights summed), with a warning.
Python package: the multislice fit could merge two different node
labels that print the same (for example 1 and
"1") when layers have unequal node sets; supra-vertices are
now keyed by (layer, node).
fit_multilayer_hungarian() matched nodes by
position, so two layers with the same named vertices stored in different
orders produced spurious label changes. Matching now uses vertex names
(positions only for unnamed layers), and the function gains
allow_unequal_nodes for layers with different named node
sets.
plot_multilayer_series() and
animate_multilayer_gif() dropped every edge of graphs with
named vertices (coordinates were indexed by name). Both now color nodes
by the tracked meta_communities rather than the layer-local
first-stage labels, interpolate the palette when there are more than
eight communities (previously an error), and the series plot uses free
panel scales.
plot_multilayer_alluvial() converted actor names to
layer-local positions, so it could connect different actors across
layers. Flows now follow actors by name, use the tracked
meta_communities, and are drawn with
ggalluvial::geom_flow() (no warning when an actor changes
community).
Documentation: objective sets only the first-stage
(per-layer) objective; the second stage always maximizes modularity
(multislice modularity for fit_multilayer_identity_ties()).
README corrections (package name, identity-tie description, five
simulator fit types).
fit_multilayer_identity_ties() (generalized Louvain
multislice): the restart-selection score omitted a factor of 2 on the
within-community edge weight, so the best of the n_starts
restarts was ranked as if the resolution were 2 rather than
resolution_parameter. Each restart already optimised the
correct objective; only the choice among restarts changes.
This release collects every change since 1.1.0 (CRAN, 2026-08-07). Versions 1.2.1 and 1.3.0 were internal and never submitted.
partition_stability(): a
reliability report for a tracked partition built from a
bootstrap_multilayer() result. It returns (i) the stability
score s, the mean NMI (or ARI) between each bootstrap
replicate’s meta-partition and the point estimate; (ii) a calibrated
accuracy floor, the 5th percentile of accuracy against the planted
partition among simulated fits with the same stability, so that accuracy
exceeded the floor in 95 percent of held-out fits; (iii) node-level
Jaccard stability with its own floor (reported only above stability
0.9); and (iv) decided node pairs (co-assignment share below/above user
thresholds). The calibration table ships in
inst/extdata/stability_calibration_table.csv and can be
overridden with calibration_table.
bootstrap_multilayer() now records
stability_samples (replicate x layer NMI and ARI to the
point estimate) and node_jaccard_stability (per-node mean
Jaccard overlap with the point-estimate community), which
partition_stability() summarises.
allow_unequal_nodes argument for
every fit_multilayer_*() function. Layers may now contain
different node sets (nodes entering and exiting the system); nodes are
matched across layers by vertex name and only nodes present in both
layers of a linked pair contribute to the interlayer similarity. Default
FALSE keeps the previous requirement of a shared node
universe.
fit_multilayer_identity_ties() now
optimises Mucha et al. (2010) multislice modularity with a generalized
Louvain (local moving plus aggregation), using each slice’s own
configuration null model k_is k_js / 2 m_s and null-free
interlayer identity ties. Previously the function ran single-graph
modularity on the stacked supra-graph, whose pooled null model is
roughly T times too small and penalises cross-slice
co-membership; at omega <= 1 that returned each slice as
one community. algorithm is kept for API compatibility but
the optimiser is always the generalized Louvain. The optimiser uses 10
random restarts (3 in the internal 1.3.0); on small change-point series
joint NMI varied by up to 0.2 across runs at 3.
weighted_jaccard_similarity() and
weighted_overlap_similarity() used
layer-wide node strengths, so a node’s strength counted toward a
community it was not a member of. Two disjoint communities could score
1.0 whenever their members had non-zero strength in both layers. A
node’s strength now counts toward community a only when the
node is a member of a (and likewise for
b).
weighted_overlap_similarity()
errored (subscript out of bounds) when a community
contained a node with no recorded strength in that layer (e.g., an
isolate). Missing strengths now contribute 0, matching
weighted_jaccard_similarity() and the Python
implementation. This affected
fit_multilayer_weighted_overlap() on layers with
isolates.
co_assignment_ci() is now
documented as a descriptive Monte Carlo interval for the bootstrap
co-assignment share, not a calibrated confidence interval. The
simulation study found pair-level intervals are not calibratable for
ambiguous pairs; use partition_stability() for a calibrated
reliability measure of the tracked partition. Function signature and
output are unchanged.
Documentation regenerated with roxygen2 7.3.3;
partition_stability help page added; cross-references
synced.
Regression tests added for the weighted similarity fixes, the
multislice null model, and partition_stability().
Uncertainty-quantification overhaul, motivated by a large-scale simulation study of empirical CI coverage (planted-partition multilayer networks; n = 50-400 nodes, 3-10 communities, 5-15 layers, 5 switching rates, 3 density regimes, Louvain and Leiden, all similarity couplings).
New method:
fit_multilayer_hungarian(). A two-stage
snapshot-and-match tracker that detects communities independently per
layer and then aligns their labels across consecutive layers with the
Hungarian (optimal linear-sum assignment) algorithm on the community
overlap matrix (clue::solve_LSAP; SciPy’s
linear_sum_assignment in the Python package). This is the
standard “independent detection + optimal label matching” baseline, now
exported as a first-class method with the same
multilayer_community_fit interface
(layer_communities, meta_communities,
extract_meta_membership()). It complements the
coupling-based fits: those jointly optimise on a coupled supra-graph,
this one matches post hoc. interlayer_ties is
NULL for this method.
Cross-layer community tracking (second-stage
detection). The fit_multilayer_*() functions now
run a second community detection on the interlayer/community graph (the
similarity ties plus self-loops) and return
meta_communities: the tracked partition grouping per-layer
communities into cross-layer meta-communities. This is what makes custom
layer_links and the interlayer coupling actually affect the
returned membership; previously the output equalled independent
per-layer detection. Access it with the new exported
extract_meta_membership(). The per-layer
layer_communities are unchanged and still returned. For the
Jaccard/overlap specifications the second stage runs on the
community-similarity graph; for the identity
specification it is Mucha (2010) multislice modularity
— the layers are stacked into one supra-graph (intra-layer edges = each
layer’s own adjacency) with interlayer identity edges, and a single
detection is run on the whole supra-graph. Custom
layer_links set the coupling in both cases.
Multislice omega / resolution-limit controls.
fit_multilayer_identity_ties() gains an omega
argument (Mucha’s interlayer coupling strength) alongside
resolution_parameter, both forwarded to the multislice
supra-graph detection. omega scales the interlayer
identity-edge weights: small values decouple toward independent
per-layer detection, omega = 1 recovers the planted
partition on well-separated networks, and large values drive the known
multislice degeneracy (temporal threads fragment or slices collapse).
Together with resolution_parameter (Mucha’s modularity
resolution) these expose the omega-sensitivity and resolution-limit
behavior of multislice modularity as tunable knobs. Mirrored in the
Python package.
Uncertainty is now quantified on the
meta-communities. bootstrap_multilayer(),
co_assignment_ci(), and community_est()
operate on the cross-layer meta-communities rather than the independent
per-layer partitions. Co-assignment now answers “do two nodes belong to
the same persistent community,” and the community count is the
number of meta-communities per layer. (Coverage of these meta-community
intervals must be re-validated in simulation; the earlier per-layer
coverage numbers do not transfer.)
seed argument for reproducible
detection. All fit_multilayer_*() functions gain a
seed argument. When supplied, the global RNG state is
saved, the RNG is seeded for the duration of the call, and the previous
state is restored on exit, so seeded detection never disturbs the
caller’s random number stream (e.g. bootstrap_multilayer()
resampling). The default (NULL) preserves the previous
behavior: detection inherits the caller’s RNG stream, so existing
scripts using set.seed() are unaffected. (In the Python
package the default is seed=123, matching its previous
internally fixed detection seed.)
Node-universe validation. Layers must now share
the same node set (compared on vertex names when present, on vertex
indices otherwise); unequal universes error with instructions instead of
silently misaligning interlayer ties.
fit_multilayer_identity_ties() gains
allow_unequal_nodes = TRUE to retain its documented support
for nodes entering or exiting the system.
Layers with different node sets are now rejected by all fit
functions (previously assumed aligned without checking). For identity
ties, opt back in with allow_unequal_nodes = TRUE.
animate_multilayer_gif() no longer has a default
output_file (previously
"multilayer_animation.gif" in the working directory). An
explicit path is now required, per CRAN policy that functions must not
write to the user’s filespace by default; use
tempfile(fileext = ".gif") for a temporary
location.
community_ci() is renamed
community_est() and no longer returns a community-count
confidence interval. The percentile community_count_ci
(estimate/lower/upper) is replaced by a community_count
data frame that reports, per layer, the observed-network
estimate and its bootstrap reproducibility
(the share of replicates whose community count equals the estimate),
plus a plain-language report. Reason: the interval covered
the truth at ~0.99 on well-specified planted-partition networks but
collapsed to ~0.62 under strong community-size skew, and no observable
diagnostic separated the reliable cases from the rest. The
reproducibility summary is descriptive and makes no coverage claim; the
package’s validated interval is co_assignment_ci(). The raw
per-replicate community counts are no longer exposed:
bootstrap_multilayer() now returns
community_count_reproducibility (the per-layer share of
replicates matching the observed count) in place of the old
community_count_samples vector.
community_ci() no longer returns
modularity_ci. The study showed its empirical coverage is
never close to the nominal 95% at any network size (~0.40 at n = 50,
0.00 at n = 100, vacuously 1.00 at n = 200): community detection
maximizes modularity, so the bootstrap interval concentrates around an
optimized, upwardly biased estimate. An interval that is
anti-conservative when detection is imperfect and uninformative when it
is exact is not a confidence interval; it has been removed rather than
documented around. Raw bootstrap draws remain available in
bootstrap_multilayer()$modularity_samples for descriptive
use.
bootstrap_multilayer() now uses a parametric network
bootstrap: within/between-community edge probabilities and edge-weight
pools are estimated from the observed network using the point-estimate
partition, and each replicate redraws the full edge set. The previous
scheme (Bayesian bootstrap on edge weights with fixed topology) was
REMOVED rather than kept as an option: because it never varies which
edges exist, it understates the variability of fresh data, and
simulation studies showed intervals built from it undercover badly
(~45-48% at nominal 95% for pairwise co-assignment) with no recovery as
networks grow. Under the project’s design principle, a misleading option
is worse than no option.
co_assignment_ci(): Wilson score intervals for
node-pair co-assignment propensities, computed from the bootstrap
co-assignment probabilities. Label-invariant, so it avoids the
label-switching problem that makes per-node membership intervals
ill-defined.
community_est() no longer issues the small-network
community-count CI warning. With the count interval removed there is no
coverage claim to qualify; the reproducibility summary is descriptive at
any network size. The co_assignment_ci() guidance to
interpret cautiously below 100 nodes remains.
directed = TRUE with
algorithm = "leiden" previously errored (igraph’s
cluster_leiden() supports undirected graphs only). Directed
layers are now collapsed to weighted undirected graphs — matching the
existing Louvain behavior — with a single warning per fit pointing users
who need directed-aware detection to the Python package
(leidenalg).
Initial CRAN release.
fit_multilayer_jaccard(),
fit_multilayer_overlap(),
fit_multilayer_weighted_jaccard(),
fit_multilayer_weighted_overlap(),
fit_multilayer_identity_ties()).layer_links,
enabling adjacent-only temporal coupling.objective argument; negative edge weights are rejected for
modularity-based methods.bootstrap_multilayer(), community_ci()).simulate_and_fit_multilayer()).plot_multilayer_series()), alluvial diagrams
(plot_multilayer_alluvial()), and animated GIFs
(animate_multilayer_gif()).These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.