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> ###############################################################################
> ## INCVCommunityDetection — Toy Example
> ##
> ## A complete walkthrough for new users demonstrating how to simulate a
> ## network, select the number of communities with INCV, and compare with
> ## ECV and NCV.
> ##
> ## Usage:
> ##   library(INCVCommunityDetection)
> ##   source("tests/toy_example.R")
> ###############################################################################
> 
> library(INCVCommunityDetection)
> 
> # ── 1. Simulate a network with 3 communities ──────────────────────
> set.seed(42)
> net <- community.sim(
+   k  = 3,      # 3 communities
+   n  = 200,    # 200 nodes
+   n1 = 60,     # smallest community has 60 nodes
+   p  = 0.4,    # within-community connection probability
+   q  = 0.05    # between-community connection probability
+ )
> 
> cat("True community sizes:\n")
True community sizes:
> print(table(net$membership))

 1  2  3 
60 70 70 
> 
> # ── 2. Select K using INCV (f-fold) ───────────────────────────────
> result <- nscv.f.fold(
+   A        = net$adjacency,
+   k.vec    = 2:7,
+   f        = 10,
+   method   = "affinity"
+ )
> 
> cat("\nINCV f-fold results:\n")

INCV f-fold results:
> cat("  K selected by loss:", result$k.loss, "\n")
  K selected by loss: 3 
> cat("  K selected by MSE: ", result$k.mse, "\n")
  K selected by MSE:  3 
> 
> # Plot the CV loss curve
> plot(2:7, result$cv.loss, type = "b", pch = 19, col = "steelblue",
+      xlab = "Number of communities (K)",
+      ylab = "CV Negative Log-Likelihood",
+      main = "INCV: Selecting the number of communities")
> abline(v = result$k.loss, lty = 2, col = "red")
> legend("topright", legend = paste("Selected K =", result$k.loss),
+        col = "red", lty = 2)
> 
> # ── 3. Select K using INCV (random split) ─────────────────────────
> result2 <- nscv.random.split(
+   A     = net$adjacency,
+   k.vec = 2:7,
+   split = 0.66,
+   ite   = 30
+ )
> 
> cat("\nINCV random-split results:\n")

INCV random-split results:
> cat("  K selected:", result2$k.chosen, "\n")
  K selected: 3 
> 
> # ── 4. Compare with ECV ───────────────────────────────────────────
> ecv <- ECV.for.blockmodel(net$adjacency, max.K = 7, B = 3)
> cat("\nECV results:\n")

ECV results:
> cat("  Model (deviance):", ecv$dev.model, "\n")
  Model (deviance): SBM-3 
> cat("  Model (L2):      ", ecv$l2.model, "\n")
  Model (L2):       SBM-3 
> 
> # ── 5. Compare with NCV ───────────────────────────────────────────
> ncv <- NCV.for.blockmodel(net$adjacency, max.K = 7, cv = 3)
> cat("\nNCV results:\n")

NCV results:
> cat("  Model (deviance):", ncv$dev.model, "\n")
  Model (deviance): SBM-3 
> cat("  Model (L2):      ", ncv$l2.model, "\n")
  Model (L2):       SBM-3 
> 
> # ── 6. Inspect the spectral clustering at the chosen K ────────────
> cl <- SBM.spectral.clustering(net$adjacency, k = result$k.loss)
> prob <- SBM.prob(cl$cluster, k = result$k.loss,
+                  A = net$adjacency, restricted = TRUE)
> 
> cat("\nEstimated block probabilities:\n")

Estimated block probabilities:
> cat("  Within-community p: ", round(prob$p.matrix[1, 1], 3), "\n")
  Within-community p:  0.397 
> cat("  Between-community q:", round(prob$p.matrix[1, 2], 3), "\n")
  Between-community q: 0.049 
> 
> # ── 7. Summary ────────────────────────────────────────────────────
> cat("\n══ Summary ══════════════════════════════════════\n")

══ Summary ══════════════════════════════════════
> cat("  True K = 3\n")
  True K = 3
> cat("  INCV f-fold  selected K =", result$k.loss, "\n")
  INCV f-fold  selected K = 3 
> cat("  INCV random  selected K =", result2$k.chosen, "\n")
  INCV random  selected K = 3 
> cat("  ECV selected:", ecv$dev.model, "\n")
  ECV selected: SBM-3 
> cat("  NCV selected:", ncv$dev.model, "\n")
  NCV selected: SBM-3 
> 
> proc.time()
   user  system elapsed 
  10.46    1.14   11.60