LCDA-ECG: ensemble-consensus community and leader detection.

Builds a pool of B randomised LCDA constructions, turns it into edge co-association weights (ECG-style), re-clusters the reweighted graph for the consensus partition, and designates one leader per community from the pool's leader-designation frequencies. Recovers planted structure on par with ECG and outperforms Leiden (advantage concentrated at high mixing), while retaining the joint leader output and a node-confidence map.

Usage

lcda_ecg(
  g,
  B = 64,
  w_min = 0.05,
  alpha_c_range = c(0.1, 0.9),
  alpha_s_range = c(0.1, 0.5),
  variant = 1,
  centrality = "eigen",
  similarity = "hpi",
  overlap = FALSE,
  tau = 0.7,
  verbose = FALSE,
  seed = NA_integer_
)

Arguments

g: an igraph object (undirected, simple).
B: pool size (number of GRASP constructions to ensemble).
w_min: ECG floor weight for 2-core edges; off-2-core edges get exactly w_min. Default 0.05, as in Poulin & Theberge (2019).
alpha_c_range, alpha_s_range: bounds of the uniform RCL parameters sampled per pool member (diversification source).
variant: construction variant, 1 or 2.
centrality, similarity: metric names passed to the construction.
overlap: logical; if TRUE, also return overlapping community memberships derived from the co-association (soft) similarity.
tau: overlap threshold in (0,1]: a node joins community c when its mean co-association to c reaches tau times its home-community affinity. Only used when overlap = TRUE.
verbose: logical; show a cli progress bar and a final summary.
seed: integer RNG seed, or NA to leave the RNG untouched.

Value

an object of class lcda_ecg_result: the consensus membership (1-based), leaders (consensus-derived, 1-based), leaders_central (top-eigenvector per community, for comparison), a per-node confidence vector, the leader-designation counts lead_count, the input-graph modularity Q (weight-aware; comparable to lcda_grasp/lcda_gr), and Q_consensus_weighted (modularity under the ECG co-association weights, i.e. the objective the consensus optimised). When overlap = TRUE it additionally carries overlap_membership (a length-n list of the community ids each node belongs to) and is_overlap (logical, the bridge nodes). It also carries the wall-clock elapsed time in seconds and the (simplified) input graph, so that lcda_metrics() and plot.lcda_ecg_result() can be called on the result alone.

Details

Weighted graphs: a numeric weight edge attribute is honoured by the modularity objective and the local search inside each pool construction, but the similarity, centrality and NCE leader score remain structural (unweighted). The consensus re-clustering uses the ECG co-association weights, not the input weights.

Examples

g <- igraph::make_graph("Zachary")
res <- lcda_ecg(g, B = 24, overlap = TRUE, tau = 0.6, seed = 1)
res$Q
#> [1] 0.4197896
which(res$is_overlap)   # bridge nodes
#> [1] 10