diff --git a/tests/testthat/_snaps/other.md b/tests/testthat/_snaps/other.md
index 44bab0e8ee5..2f5090f3c93 100644
--- a/tests/testthat/_snaps/other.md
+++ b/tests/testthat/_snaps/other.md
@@ -26,7 +26,7 @@
 # VS/ES require explicit conversion
 
     Code
-      V(karate_oldstyle)
+      V(karate_oldstyle_graph())
     Condition
       Error in `warn_version()`:
       ! This graph was created by a now unsupported old igraph version.
diff --git a/tests/testthat/helper-test-functions.R b/tests/testthat/helper-test-functions.R
index 692f0d1a345..ed96615d253 100644
--- a/tests/testthat/helper-test-functions.R
+++ b/tests/testthat/helper-test-functions.R
@@ -17,43 +17,78 @@ standardize_eigen_signs <- function(x) {
   })
 }
 
-order_by_magnitude <- function(x) {
+order_eigenvalues_by_magnitude <- function(x) {
   order(abs(x), sign(x), decreasing = TRUE)
 }
 
-sort_by_magnitude <- function(x) {
-  x[order_by_magnitude(x)]
+sort_eigenvalues_by_magnitude <- function(x) {
+  x[order_eigenvalues_by_magnitude(x)]
 }
 
 # ---- test-operators.R -------------------------------------------------------
 
-order_by_two_first_columns <- function(x) x[order(x[, 1], x[, 2]), ]
+sort_edgelist_rows <- function(x) x[order(x[, 1], x[, 2]), ]
 
-rn <- function(D) {
+name_rows_by_edge_endpoints <- function(D) {
   rownames(D) <- paste(D[, 1], D[, 2], sep = "-")
   D
 }
 
-# Input/expected pairs for the unique()-on-vertex-sequence tests.
-unique_tests <- list(
-  list(1:5, 1:5),
-  list(c(1, 1, 2:5), 1:5),
-  list(c(1, 1, 1, 1), 1),
-  list(c(1, 2, 2, 2), 1:2),
-  list(c(2, 2, 1, 1), 2:1),
-  list(c(1, 2, 1, 2), 1:2),
-  list(c(), c())
-)
+# Input/expected vertex-index pairs for the unique()-on-vertex-sequence tests:
+# each element is `list(<indices to select>, <indices left after unique()>)`.
+unique_vertex_seq_cases <- function() {
+  list(
+    list(1:5, 1:5),
+    list(c(1, 1, 2:5), 1:5),
+    list(c(1, 1, 1, 1), 1),
+    list(c(1, 2, 2, 2), 1:2),
+    list(c(2, 2, 1, 1), 2:1),
+    list(c(1, 2, 1, 2), 1:2),
+    list(c(), c())
+  )
+}
+
+# A fresh already-simple graph with two edge attributes, one of which the
+# default combination list keeps and one of which it drops. Each caller needs
+# its own: the C core's property cache lives in the graph object, and merely
+# asking whether the graph is simple changes what simplifying it does.
+simple_graph_with_edge_attrs <- function() {
+  g <- make_graph(c(1, 2, 2, 3), directed = FALSE)
+  E(g)$weight <- c(1, 2)
+  E(g)$foo <- c("a", "b")
+  g
+}
 
 # ---- test-glet.R ------------------------------------------------------------
 
-sortgl <- function(x) {
+# Shared fixture: the weighted overlapping-groups graph from the examples.
+# Its `weight` edge attribute has four distinct threshold levels.
+make_weighted_graphlet_graph <- function() {
+  D1 <- matrix(0, 5, 5)
+  D2 <- matrix(0, 5, 5)
+  D3 <- matrix(0, 5, 5)
+  D1[1:3, 1:3] <- 2
+  D2[3:5, 3:5] <- 3
+  D3[2:5, 2:5] <- 1
+  simplify(graph_from_adjacency_matrix(
+    D1 + D2 + D3,
+    mode = "undirected",
+    weighted = TRUE
+  ))
+}
+
+# Canonicalise a graphlet_basis() result for comparison: sort the vertices
+# within each clique, then the cliques by size (carrying their thresholds).
+sort_graphlets_by_size <- function(x) {
   cl <- lapply(x$cliques, sort)
   n <- lengths(cl)
   list(cliques = cl[order(n)], thresholds = x$thresholds[order(n)])
 }
 
-threshold.net <- function(graph, level) {
+# The maximal cliques of the subgraph left after dropping every edge whose
+# weight is below `level`, largest first. One thresholding step of
+# graphlet_basis_reference() below.
+max_cliques_above_weight <- function(graph, level) {
   graph.t <- delete_edges(graph, which(E(graph)$weight < level))
 
   clqt <- unvs(max_cliques(graph.t))
@@ -61,7 +96,9 @@ threshold.net <- function(graph, level) {
   clqt[order(lengths(clqt), decreasing = TRUE)]
 }
 
-graphlets.old <- function(graph) {
+# Pure-R reference implementations of graphlet_basis() and graphlet_proj(),
+# kept to cross-check the C results.
+graphlet_basis_reference <- function(graph) {
   if (!is_weighted(graph)) {
     cli::cli_abort("Graph not weighted")
   }
@@ -71,7 +108,7 @@ graphlets.old <- function(graph) {
 
   ## Do all thresholds
   cl <- lapply(sort(unique(E(graph)$weight)), function(w) {
-    threshold.net(graph, w)
+    max_cliques_above_weight(graph, w)
   })
 
   ## Put the cliques in one long list
@@ -89,7 +126,7 @@ graphlets.old <- function(graph) {
   clf
 }
 
-graphlets.project.old <- function(graph, cliques, iter, Mu = NULL) {
+graphlet_proj_reference <- function(graph, cliques, iter, Mu = NULL) {
   if (!is_weighted(graph)) {
     cli::cli_abort("Graph not weighted")
   }
@@ -161,94 +198,150 @@ graphlets.project.old <- function(graph, cliques, iter, Mu = NULL) {
 # that VS/ES require (and survive) an explicit upgrade. Renamed from the
 # file-local `names`/`karate` to avoid shadowing base `names()` once sourced
 # into the shared testthat environment.
-karate_oldstyle_names <- c(
-  "Mr Hi", "Actor 2", "Actor 3", "Actor 4",
-  "Actor 5", "Actor 6", "Actor 7", "Actor 8", "Actor 9", "Actor 10",
-  "Actor 11", "Actor 12", "Actor 13", "Actor 14", "Actor 15", "Actor 16",
-  "Actor 17", "Actor 18", "Actor 19", "Actor 20", "Actor 21", "Actor 22",
-  "Actor 23", "Actor 24", "Actor 25", "Actor 26", "Actor 27", "Actor 28",
-  "Actor 29", "Actor 30", "Actor 31", "Actor 32", "Actor 33", "John A"
-)
-
-karate_oldstyle <- structure(
-  list(
-    34,
-    FALSE,
-    c(
-      1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12,
-      13, 17, 19, 21, 31, 2, 3, 7, 13, 17, 19, 21, 30, 3, 7, 8, 9,
-      13, 27, 28, 32, 7, 12, 13, 6, 10, 6, 10, 16, 16, 30, 32, 33,
-      33, 33, 32, 33, 32, 33, 32, 33, 33, 32, 33, 32, 33, 25, 27, 29,
-      32, 33, 25, 27, 31, 31, 29, 33, 33, 31, 33, 32, 33, 32, 33, 32,
-      33, 33
-    ),
-    c(
-      0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
-      1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5,
-      5, 5, 6, 8, 8, 8, 9, 13, 14, 14, 15, 15, 18, 18, 19, 20, 20,
-      22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 25, 26, 26, 27, 28, 28,
-      29, 29, 30, 30, 31, 31, 32
-    ),
-    c(
-      0, 1, 16, 2, 17, 24, 3, 4, 5,
-      35, 37, 6, 18, 25, 32, 7, 26, 27, 8, 36, 38, 9, 10, 33, 11, 19,
-      28, 34, 39, 40, 12, 20, 13, 21, 14, 22, 57, 62, 29, 58, 63, 30,
-      59, 66, 23, 41, 15, 64, 65, 69, 31, 42, 46, 48, 50, 53, 55, 60,
-      71, 73, 75, 43, 44, 45, 47, 49, 51, 52, 54, 56, 61, 67, 68, 70,
-      72, 74, 76, 77
-    ),
-    c(
-      0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
-      13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
-      29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,
-      45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
-      61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
-      77
-    ),
-    c(
-      0, 0, 1, 3, 6, 7, 8, 11, 15, 17, 18, 21, 22, 24, 28, 28,
-      28, 30, 32, 32, 34, 34, 36, 36, 36, 36, 38, 38, 41, 42, 44, 46,
-      50, 61, 78
-    ),
-    c(
-      0, 16, 24, 32, 35, 37, 40, 41, 41, 44, 45, 45,
-      45, 45, 46, 48, 50, 50, 50, 52, 53, 55, 55, 57, 62, 65, 66, 68,
-      69, 71, 73, 75, 77, 78, 78
-    ),
+karate_oldstyle_vertex_names <- function() {
+  c(
+    "Mr Hi", "Actor 2", "Actor 3", "Actor 4",
+    "Actor 5", "Actor 6", "Actor 7", "Actor 8", "Actor 9", "Actor 10",
+    "Actor 11", "Actor 12", "Actor 13", "Actor 14", "Actor 15", "Actor 16",
+    "Actor 17", "Actor 18", "Actor 19", "Actor 20", "Actor 21", "Actor 22",
+    "Actor 23", "Actor 24", "Actor 25", "Actor 26", "Actor 27", "Actor 28",
+    "Actor 29", "Actor 30", "Actor 31", "Actor 32", "Actor 33", "John A"
+  )
+}
+
+karate_oldstyle_graph <- function() {
+  structure(
     list(
-      c(1, 0, 1),
-      structure(
-        list(
-          name = "Zachary's karate club network",
-          Citation = "Wayne W. Zachary. An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research Vol. 33, No. 4 452-473",
-          Author = "Wayne W. Zachary"
-        ),
-        names = c("name", "Citation", "Author")
+      34,
+      FALSE,
+      c(
+        1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12,
+        13, 17, 19, 21, 31, 2, 3, 7, 13, 17, 19, 21, 30, 3, 7, 8, 9,
+        13, 27, 28, 32, 7, 12, 13, 6, 10, 6, 10, 16, 16, 30, 32, 33,
+        33, 33, 32, 33, 32, 33, 32, 33, 33, 32, 33, 32, 33, 25, 27, 29,
+        32, 33, 25, 27, 31, 31, 29, 33, 33, 31, 33, 32, 33, 32, 33, 32,
+        33, 33
+      ),
+      c(
+        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
+        1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 5,
+        5, 5, 6, 8, 8, 8, 9, 13, 14, 14, 15, 15, 18, 18, 19, 20, 20,
+        22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 25, 26, 26, 27, 28, 28,
+        29, 29, 30, 30, 31, 31, 32
+      ),
+      c(
+        0, 1, 16, 2, 17, 24, 3, 4, 5,
+        35, 37, 6, 18, 25, 32, 7, 26, 27, 8, 36, 38, 9, 10, 33, 11, 19,
+        28, 34, 39, 40, 12, 20, 13, 21, 14, 22, 57, 62, 29, 58, 63, 30,
+        59, 66, 23, 41, 15, 64, 65, 69, 31, 42, 46, 48, 50, 53, 55, 60,
+        71, 73, 75, 43, 44, 45, 47, 49, 51, 52, 54, 56, 61, 67, 68, 70,
+        72, 74, 76, 77
+      ),
+      c(
+        0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
+        13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28,
+        29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44,
+        45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60,
+        61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
+        77
+      ),
+      c(
+        0, 0, 1, 3, 6, 7, 8, 11, 15, 17, 18, 21, 22, 24, 28, 28,
+        28, 30, 32, 32, 34, 34, 36, 36, 36, 36, 38, 38, 41, 42, 44, 46,
+        50, 61, 78
       ),
-      structure(
-        list(
-          Faction = c(
-            1, 1, 1, 1, 1, 1, 1, 1,
-            2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2,
-            2, 2, 2, 2, 2
+      c(
+        0, 16, 24, 32, 35, 37, 40, 41, 41, 44, 45, 45,
+        45, 45, 46, 48, 50, 50, 50, 52, 53, 55, 55, 57, 62, 65, 66, 68,
+        69, 71, 73, 75, 77, 78, 78
+      ),
+      list(
+        c(1, 0, 1),
+        structure(
+          list(
+            name = "Zachary's karate club network",
+            Citation = "Wayne W. Zachary. An Information Flow Model for Conflict and Fission in Small Groups. Journal of Anthropological Research Vol. 33, No. 4 452-473",
+            Author = "Wayne W. Zachary"
           ),
-          name = karate_oldstyle_names
+          names = c("name", "Citation", "Author")
         ),
-        names = c("Faction", "name")
-      ),
-      structure(
-        list(
-          weight = c(
-            4,
-            5, 3, 3, 3, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 6, 3, 4, 5, 1, 2,
-            2, 2, 3, 4, 5, 1, 3, 2, 2, 2, 3, 3, 3, 2, 3, 5, 3, 3, 3, 3, 3,
-            4, 2, 3, 3, 2, 3, 4, 1, 2, 1, 3, 1, 2, 3, 5, 4, 3, 5, 4, 2, 3,
-            2, 7, 4, 2, 4, 2, 2, 4, 2, 3, 3, 4, 4, 5
-          )
+        structure(
+          list(
+            Faction = c(
+              1, 1, 1, 1, 1, 1, 1, 1,
+              2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2,
+              2, 2, 2, 2, 2
+            ),
+            name = karate_oldstyle_vertex_names()
+          ),
+          names = c("Faction", "name")
         ),
-        names = "weight"
+        structure(
+          list(
+            weight = c(
+              4,
+              5, 3, 3, 3, 3, 2, 2, 2, 3, 1, 3, 2, 2, 2, 2, 6, 3, 4, 5, 1, 2,
+              2, 2, 3, 4, 5, 1, 3, 2, 2, 2, 3, 3, 3, 2, 3, 5, 3, 3, 3, 3, 3,
+              4, 2, 3, 3, 2, 3, 4, 1, 2, 1, 3, 1, 2, 3, 5, 4, 3, 5, 4, 2, 3,
+              2, 7, 4, 2, 4, 2, 2, 4, 2, 3, 3, 4, 4, 5
+            )
+          ),
+          names = "weight"
+        )
       )
-    )
-  ),
-  class = "igraph"
-)
+    ),
+    class = "igraph"
+  )
+}
+
+# ---- test-cliques.R ---------------------------------------------------------
+
+# Shared fixture: a triangle plus a disjoint edge.
+# The `weight` vertex attribute favors the edge,
+# an explicit weight vector can flip the result to the triangle.
+make_weighted_clique_graph <- function() {
+  g <- make_full_graph(3) %du% make_full_graph(2)
+  V(g)$weight <- c(1, 1, 1, 4, 4)
+  g
+}
+
+# ---- test-decomposition.R ---------------------------------------------------
+
+# The first example graph from the Tarjan-Yannakakis paper.
+tarjan_yannakakis_graph <- function() {
+  graph_from_literal(
+    A - B:C:I, B - A:C:D, C - A:B:E:H, D - B:E:F,
+    E - C:D:F:H, F - D:E:G, G - F:H, H - C:E:G:I,
+    I - A:H
+  )
+}
+
+# ---- test-generate-migrations.R ---------------------------------------------
+
+# Source the ellipsis-migration generator into a fresh environment and return
+# it. The generator only exists in a source checkout (tools/ is
+# .Rbuildignore'd), so the caller is skipped when it is missing.
+load_migration_generator <- function() {
+  generator <- testthat::test_path("..", "..", "tools", "generate-migrations.R")
+  skip_if_not(file.exists(generator), "tools/generate-migrations.R not found")
+  gen_env <- new.env()
+  sys.source(generator, envir = gen_env)
+  gen_env
+}
+
+# Write a throw-away registry file and return its path.
+write_migration_registry <- function(dir, name, code) {
+  path <- file.path(dir, name)
+  writeLines(code, path)
+  path
+}
+
+# ---- test-hrg.R -------------------------------------------------------------
+
+# A compact shared fixture: a tiny two-clique graph and one HRG fitted to it,
+# reused by the consensus_tree() and predict_edges() blocks.
+# Fitting a real HRG is the awkward part of constructing valid inputs there.
+hrg_graph_and_fit <- function() {
+  g <- make_full_graph(4) + make_full_graph(4)
+  igraph_with_seed(1, list(graph = g, hrg = fit_hrg(g)))
+}
diff --git a/tests/testthat/test-cliques.R b/tests/testthat/test-cliques.R
index 9d14e3d84a2..54a3beb4015 100644
--- a/tests/testthat/test-cliques.R
+++ b/tests/testthat/test-cliques.R
@@ -462,14 +462,8 @@ test_that("max_cliques handles errors in callback", {
 
 # ---- ellipsis migration: argument coverage ----------------------------
 
-# Shared fixture: a triangle plus a disjoint edge.
-# The `weight` vertex attribute favors the edge,
-# an explicit weight vector can flip the result to the triangle.
-make_weighted_clique_graph <- function() {
-  g <- make_full_graph(3) %du% make_full_graph(2)
-  V(g)$weight <- c(1, 1, 1, 4, 4)
-  g
-}
+# The `make_weighted_clique_graph()` fixture used below lives in
+# helper-test-functions.R.
 
 test_that("clique_size_counts() recovers legacy positional arguments", {
   # `min`, `max` and `maximal` are exercised by name above.
diff --git a/tests/testthat/test-decomposition.R b/tests/testthat/test-decomposition.R
index a79f095fd0d..9c5fd13bddb 100644
--- a/tests/testthat/test-decomposition.R
+++ b/tests/testthat/test-decomposition.R
@@ -43,14 +43,9 @@ test_that("is_chordal works", {
 
 # ---- ellipsis migration: argument coverage ----------------------------
 
-# The first example graph from the Tarjan-Yannakakis paper, as in the test above.
-tarjan_yannakakis_graph <- function() {
-  graph_from_literal(
-    A - B:C:I, B - A:C:D, C - A:B:E:H, D - B:E:F,
-    E - C:D:F:H, F - D:E:G, G - F:H, H - C:E:G:I,
-    I - A:H
-  )
-}
+# The `tarjan_yannakakis_graph()` fixture used below -- the first example graph
+# from the Tarjan-Yannakakis paper, as in the test above -- lives in
+# helper-test-functions.R.
 
 test_that("is_chordal accepts alpha, alpham1, fillin, and newgraph by name", {
   g <- tarjan_yannakakis_graph()
diff --git a/tests/testthat/test-embedding.R b/tests/testthat/test-embedding.R
index 16be97fb8ad..739c2a06c45 100644
--- a/tests/testthat/test-embedding.R
+++ b/tests/testthat/test-embedding.R
@@ -51,15 +51,17 @@ test_that("embed_adjacency_matrix -- Undirected, unweighted case works", {
     scaled = FALSE
   )
 
-  expect_equal(as_lm$D, sort_by_magnitude(ss$values)[1:no])
-  expect_equal(au_lm$D, sort_by_magnitude(ss$values)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(ss$values)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(ss$values)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(ss$values)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(ss$values)][,
+      1:no
+    ])
   )
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    X[, order_by_magnitude(ss$values)][, 1:no]
+    X[, order_eigenvalues_by_magnitude(ss$values)][, 1:no]
   )
 
   au_sa <- embed_adjacency_matrix(
@@ -138,15 +140,17 @@ test_that("embed_adjacency_matrix -- Undirected, weighted case works", {
     scaled = FALSE
   )
 
-  expect_equal(as_lm$D, sort_by_magnitude(ss$values)[1:no])
-  expect_equal(au_lm$D, sort_by_magnitude(ss$values)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(ss$values)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(ss$values)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(ss$values)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(ss$values)][,
+      1:no
+    ])
   )
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    X[, order_by_magnitude(ss$values)][, 1:no]
+    X[, order_eigenvalues_by_magnitude(ss$values)][, 1:no]
   )
 
   au_sa <- embed_adjacency_matrix(
@@ -452,15 +456,15 @@ test_that("embed_laplacian_matrix -- Undirected, unweighted, D-A case works", {
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
@@ -551,15 +555,15 @@ test_that("embed_laplacian_matrix -- Undirected, unweighted, DAD case works", {
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
@@ -650,15 +654,15 @@ test_that("embed_laplacian_matrix -- Undirected, unweighted, I-DAD case works",
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
@@ -750,15 +754,15 @@ test_that("embed_laplacian_matrix -- Undirected, weighted, D-A case works", {
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
@@ -847,15 +851,15 @@ test_that("embed_laplacian_matrix -- Undirected, unweighted, DAD case works", {
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
@@ -947,15 +951,15 @@ test_that("embed_laplacian_matrix -- Undirected, unweighted, I-DAD case works",
     scaled = FALSE
   )
 
-  expect_equal(au_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(au_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(au_lm$X),
-    standardize_eigen_signs(X[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(X[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
-  expect_equal(as_lm$D, sort_by_magnitude(D)[1:no])
+  expect_equal(as_lm$D, sort_eigenvalues_by_magnitude(D)[1:no])
   expect_equal(
     standardize_eigen_signs(as_lm$X),
-    standardize_eigen_signs(U[, order_by_magnitude(D)][, 1:no])
+    standardize_eigen_signs(U[, order_eigenvalues_by_magnitude(D)][, 1:no])
   )
 
   ## SA
diff --git a/tests/testthat/test-generate-migrations.R b/tests/testthat/test-generate-migrations.R
index c1146679b21..a661c1e33a3 100644
--- a/tests/testthat/test-generate-migrations.R
+++ b/tests/testthat/test-generate-migrations.R
@@ -2,38 +2,27 @@
 # The generator is plain base R and only exists in a source checkout
 # (tools/ is .Rbuildignore'd), so these tests are skipped in a built package.
 
-local_generator <- function(env = parent.frame()) {
-  generator <- testthat::test_path("..", "..", "tools", "generate-migrations.R")
-  skip_if_not(file.exists(generator), "tools/generate-migrations.R not found")
-  gen_env <- new.env()
-  sys.source(generator, envir = gen_env)
-  gen_env
-}
-
-write_registry <- function(dir, name, code) {
-  path <- file.path(dir, name)
-  writeLines(code, path)
-  path
-}
+# The `load_migration_generator()` and `write_migration_registry()` helpers
+# used below live in helper-test-functions.R.
 
 test_that("migration_registry_files() finds the legacy file and topic files", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   root <- withr::local_tempdir()
   dir.create(file.path(root, "tools", "migrations"), recursive = TRUE)
 
   expect_identical(gen$migration_registry_files(root), character(0))
 
-  legacy <- write_registry(
+  legacy <- write_migration_registry(
     file.path(root, "tools"),
     "migrations.R",
     "migrations <- list()"
   )
-  b <- write_registry(
+  b <- write_migration_registry(
     file.path(root, "tools", "migrations"),
     "b-topic.R",
     "migrations <- list()"
   )
-  a <- write_registry(
+  a <- write_migration_registry(
     file.path(root, "tools", "migrations"),
     "a-topic.R",
     "migrations <- list()"
@@ -44,10 +33,10 @@ test_that("migration_registry_files() finds the legacy file and topic files", {
 })
 
 test_that("load_migrations() merges entries across registry files", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   dir <- withr::local_tempdir()
 
-  one <- write_registry(
+  one <- write_migration_registry(
     dir,
     "one.R",
     c(
@@ -60,7 +49,7 @@ test_that("load_migrations() merges entries across registry files", {
       ")"
     )
   )
-  two <- write_registry(
+  two <- write_migration_registry(
     dir,
     "two.R",
     c(
@@ -80,7 +69,7 @@ test_that("load_migrations() merges entries across registry files", {
 })
 
 test_that("load_migrations() rejects duplicate entries across files", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   dir <- withr::local_tempdir()
 
   entry <- c(
@@ -92,8 +81,8 @@ test_that("load_migrations() rejects duplicate entries across files", {
     "  )",
     ")"
   )
-  one <- write_registry(dir, "one.R", entry)
-  two <- write_registry(dir, "two.R", entry)
+  one <- write_migration_registry(dir, "one.R", entry)
+  two <- write_migration_registry(dir, "two.R", entry)
 
   expect_error(
     gen$load_migrations(c(one, two)),
@@ -102,10 +91,10 @@ test_that("load_migrations() rejects duplicate entries across files", {
 })
 
 test_that("load_migrations() rejects files without a migrations list", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   dir <- withr::local_tempdir()
 
-  bad <- write_registry(dir, "bad.R", "not_migrations <- list()")
+  bad <- write_migration_registry(dir, "bad.R", "not_migrations <- list()")
   expect_error(
     gen$load_migrations(bad),
     "must define a `migrations` list"
@@ -113,10 +102,10 @@ test_that("load_migrations() rejects files without a migrations list", {
 })
 
 test_that("load_migrations() tolerates empty registries", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   dir <- withr::local_tempdir()
 
-  empty <- write_registry(dir, "empty.R", "migrations <- list()")
+  empty <- write_migration_registry(dir, "empty.R", "migrations <- list()")
   expect_identical(gen$load_migrations(empty), list())
   expect_identical(gen$load_migrations(character(0)), list())
 })
@@ -125,7 +114,7 @@ test_that("default expressions keep air's spacing around binary `/`", {
   # The constant-defaults rule keeps arithmetic like `n / 7100` out of real
   # registries, but the renderer must stay air-clean for any deparsed
   # expression, so exercise the helpers directly.
-  gen <- local_generator()
+  gen <- load_migration_generator()
   fmls <- formals(function(agebins = n / 7100, base = "http://a/b") {})
   expect_identical(gen$default_expr(fmls, "agebins"), "n / 7100")
   # slashes inside string literals stay untouched
@@ -133,7 +122,7 @@ test_that("default expressions keep air's spacing around binary `/`", {
 })
 
 test_that("is_constant_default() classifies expressions", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   const <- alist(
     NULL,
     TRUE,
@@ -184,7 +173,7 @@ test_that("is_constant_default() classifies expressions", {
 })
 
 test_that("non-constant defaults are rejected, with no escape hatch", {
-  gen <- local_generator()
+  gen <- load_migration_generator()
   entry <- list(
     old = function(graph, vids) {},
     new = function(graph, ..., vids = V(graph)) {},
diff --git a/tests/testthat/test-glet.R b/tests/testthat/test-glet.R
index af039389da0..09dace2b8a7 100644
--- a/tests/testthat/test-glet.R
+++ b/tests/testthat/test-glet.R
@@ -11,7 +11,7 @@ test_that("Graphlets work for some simple graphs", {
   expect_equal(full_glet$thresholds, 1)
 
   E(full)[1 %--% 2]$weight <- 2
-  full_glet2 <- sortgl(graphlet_basis(full))
+  full_glet2 <- sort_graphlets_by_size(graphlet_basis(full))
 
   expect_equal(
     full_glet2,
@@ -39,7 +39,7 @@ test_that("Graphlets filtering works", {
     directed = FALSE,
     vertices = data.frame(LETTERS[1:5])
   )
-  glet <- sortgl(graphlet_basis(g))
+  glet <- sort_graphlets_by_size(graphlet_basis(g))
 
   expect_equal(unvs(glet$cliques), list(1:3, 2:5))
   expect_equal(glet$thresholds, c(8, 5))
@@ -51,7 +51,7 @@ test_that("Graphlets work for a bigger graph", {
   E(g)$weight <- sample(1:5, ecount(g), replace = TRUE)
 
   gl <- graphlet_basis(g)
-  gl2 <- graphlets.old(g)
+  gl2 <- graphlet_basis_reference(g)
 
   glo <- sort(sapply(unvs(gl$cliques), paste, collapse = "-"))
   gl2o <- sort(sapply(gl2, paste, collapse = "-"))
@@ -75,31 +75,18 @@ test_that("Graphlet projection works", {
 
   gl <- graphlet_basis(g)
   glp <- graphlets(g)
-  glp2 <- graphlets.project.old(g, cliques = gl$cliques, iter = 1000)
+  glp2 <- graphlet_proj_reference(g, cliques = gl$cliques, iter = 1000)
 
   expect_equal(glp, glp2)
 })
 
 # ---- ellipsis migration: argument coverage ----------------------------
 
-# Shared fixture: the weighted overlapping-groups graph from the examples.
-# Its `weight` edge attribute has four distinct threshold levels.
-make_graphlet_graph <- function() {
-  D1 <- matrix(0, 5, 5)
-  D2 <- matrix(0, 5, 5)
-  D3 <- matrix(0, 5, 5)
-  D1[1:3, 1:3] <- 2
-  D2[3:5, 3:5] <- 3
-  D3[2:5, 2:5] <- 1
-  simplify(graph_from_adjacency_matrix(
-    D1 + D2 + D3,
-    mode = "undirected",
-    weighted = TRUE
-  ))
-}
+# The `make_weighted_graphlet_graph()` fixture used below lives in
+# helper-test-functions.R.
 
 test_that("graphlet_basis() covers weights", {
-  g <- make_graphlet_graph()
+  g <- make_weighted_graphlet_graph()
 
   # The attribute weights yield a four-clique candidate basis,
   # uniform explicit weights override them and collapse the basis
@@ -118,7 +105,7 @@ test_that("graphlet_basis() covers weights", {
 })
 
 test_that("graphlet_proj() covers all tail arguments", {
-  g <- make_graphlet_graph()
+  g <- make_weighted_graphlet_graph()
   cl <- graphlet_basis(g)$cliques
 
   # The projection returns one non-negative weight per basis clique.
@@ -144,7 +131,7 @@ test_that("graphlet_proj() covers all tail arguments", {
 })
 
 test_that("graphlets() covers all tail arguments", {
-  g <- make_graphlet_graph()
+  g <- make_weighted_graphlet_graph()
   w <- rep(1, ecount(g))
 
   # Uniform weights collapse the basis to the two maximal cliques.
diff --git a/tests/testthat/test-hrg.R b/tests/testthat/test-hrg.R
index 215a0e7cb50..eaf8b8478aa 100644
--- a/tests/testthat/test-hrg.R
+++ b/tests/testthat/test-hrg.R
@@ -141,17 +141,11 @@ test_that("print.igrapHRG() works", {
 
 # ---- ellipsis migration: argument coverage ----------------------------
 
-# A compact shared fixture: a tiny two-clique graph and one HRG fitted to it,
-# reused by the consensus_tree() and predict_edges() blocks below.
-# Fitting a real HRG is the awkward part of constructing valid inputs there.
-hrg_fixture <- function() {
-  g <- make_full_graph(4) + make_full_graph(4)
-  igraph_with_seed(1, list(graph = g, hrg = fit_hrg(g)))
-}
+# The `hrg_graph_and_fit()` fixture used below lives in helper-test-functions.R.
 
 test_that("fit_hrg() recovers a legacy positional argument", {
   rlang::local_options(lifecycle_verbosity = "warning")
-  fx <- hrg_fixture()
+  fx <- hrg_graph_and_fit()
 
   igraph_local_seed(2)
   lifecycle::expect_deprecated(
@@ -162,7 +156,7 @@ test_that("fit_hrg() recovers a legacy positional argument", {
 })
 
 test_that("consensus_tree() covers keyword-only tail arguments", {
-  fx <- hrg_fixture()
+  fx <- hrg_graph_and_fit()
   igraph_local_seed(3)
 
   res <- consensus_tree(fx$graph, hrg = fx$hrg, start = TRUE, num.samples = 100)
@@ -173,7 +167,7 @@ test_that("consensus_tree() covers keyword-only tail arguments", {
 
 test_that("consensus_tree() recovers a legacy positional argument", {
   rlang::local_options(lifecycle_verbosity = "warning")
-  fx <- hrg_fixture()
+  fx <- hrg_graph_and_fit()
 
   # `num.samples` is pinned small (by name) to keep the two runs fast; `start`
   # is the recovered positional argument.
@@ -189,7 +183,7 @@ test_that("consensus_tree() recovers a legacy positional argument", {
 })
 
 test_that("predict_edges() covers keyword-only tail arguments", {
-  fx <- hrg_fixture()
+  fx <- hrg_graph_and_fit()
   igraph_local_seed(5)
 
   res <- predict_edges(
@@ -206,7 +200,7 @@ test_that("predict_edges() covers keyword-only tail arguments", {
 
 test_that("predict_edges() recovers a legacy positional argument", {
   rlang::local_options(lifecycle_verbosity = "warning")
-  fx <- hrg_fixture()
+  fx <- hrg_graph_and_fit()
 
   igraph_local_seed(6)
   lifecycle::expect_deprecated(
diff --git a/tests/testthat/test-operators.R b/tests/testthat/test-operators.R
index d818c2089d5..557a7005b69 100644
--- a/tests/testthat/test-operators.R
+++ b/tests/testthat/test-operators.R
@@ -6,8 +6,8 @@ test_that("union() works", {
   expect_vcount(gu, 11)
   expect_ecount(gu, 20)
   expect_equal(
-    order_by_two_first_columns(rbind(as_edgelist(g1), as_edgelist(g2))),
-    order_by_two_first_columns(as_edgelist(gu))
+    sort_edgelist_rows(rbind(as_edgelist(g1), as_edgelist(g2))),
+    sort_edgelist_rows(as_edgelist(gu))
   )
   expect_isomorphic(difference(gu, g1), g2)
   expect_isomorphic(intersection(gu, g2), g2)
@@ -18,8 +18,8 @@ test_that("disjoint_union() works", {
   g2 <- make_star(11, center = 11, mode = "undirected")
   gdu <- disjoint_union(g1, g2)
   expect_equal(
-    order_by_two_first_columns(as_edgelist(gdu)),
-    order_by_two_first_columns(rbind(
+    sort_edgelist_rows(as_edgelist(gdu)),
+    sort_edgelist_rows(rbind(
       as_edgelist(g1),
       as_edgelist(g2) + vcount(g1)
     ))
@@ -664,9 +664,9 @@ test_that("intersection of non-named graphs keeps attributes properly", {
 
   gi <- intersection(g, g2)
 
-  df <- rn(as_data_frame(g))
-  df2 <- rn(as_data_frame(g2))
-  dfi <- rn(as_data_frame(gi))
+  df <- name_rows_by_edge_endpoints(as_data_frame(g))
+  df2 <- name_rows_by_edge_endpoints(as_data_frame(g2))
+  dfi <- name_rows_by_edge_endpoints(as_data_frame(gi))
 
   expect_equal(df[rownames(dfi), ], dfi[, 1:3], ignore_attr = TRUE)
   expect_equal(df2[rownames(dfi), ], dfi[, c(1, 2, 4)], ignore_attr = TRUE)
@@ -682,9 +682,9 @@ test_that("union of non-named graphs keeps attributes properly", {
 
   gu <- union.igraph(g, g2)
 
-  df <- rn(as_data_frame(g))
-  df2 <- rn(as_data_frame(g2))
-  dfu <- rn(as_data_frame(gu))
+  df <- name_rows_by_edge_endpoints(as_data_frame(g))
+  df2 <- name_rows_by_edge_endpoints(as_data_frame(g2))
+  dfu <- name_rows_by_edge_endpoints(as_data_frame(gu))
 
   expect_equal(dfu[rownames(df), 1:3], df, ignore_attr = TRUE)
   expect_equal(dfu[rownames(df2), c(1, 2, 4)], df2, ignore_attr = TRUE)
@@ -1248,11 +1248,11 @@ test_that("rev on detached vs, names", {
   }
 })
 
-# `unique_tests` (the input/expected pairs used below) lives in
+# `unique_vertex_seq_cases()` (the input/expected pairs used below) lives in
 # helper-test-functions.R.
 
 test_that("unique on attached vs", {
-  sapply(unique_tests, function(d) {
+  sapply(unique_vertex_seq_cases(), function(d) {
     g <- make_ring(10)
     vg <- unique(V(g)[d[[1]]])
     vr <- V(g)[d[[2]]]
@@ -1261,7 +1261,7 @@ test_that("unique on attached vs", {
 })
 
 test_that("unique on detached vs", {
-  sapply(unique_tests, function(d) {
+  sapply(unique_vertex_seq_cases(), function(d) {
     g <- make_ring(10)
     vg <- V(g)[d[[1]]]
     vr <- V(g)[d[[2]]]
@@ -1273,7 +1273,7 @@ test_that("unique on detached vs", {
 })
 
 test_that("unique on attached vs, names", {
-  sapply(unique_tests, function(d) {
+  sapply(unique_vertex_seq_cases(), function(d) {
     g <- make_ring(10)
     V(g)$name <- letters[1:10]
     vg <- unique(V(g)[d[[1]]])
@@ -1283,7 +1283,7 @@ test_that("unique on attached vs, names", {
 })
 
 test_that("unique on detached vs, names", {
-  sapply(unique_tests, function(d) {
+  sapply(unique_vertex_seq_cases(), function(d) {
     g <- make_ring(10)
     V(g)$name <- letters[1:10]
     vg <- V(g)[d[[1]]]
@@ -1405,17 +1405,8 @@ test_that("graph.attr.comb defaults to the graph.attr.comb igraph option", {
   expect_length(graph_attr_names(compose(g1, g2)), 0)
 })
 
-# A fresh already-simple graph with two edge attributes, one of which the
-# default combination list keeps and one of which it drops. Each caller needs
-# its own: the C core's property cache lives in the graph object, and merely
-# asking whether the graph is simple changes what simplifying it does -- see
-# the second test below.
-simple_graph_with_attrs <- function() {
-  g <- make_graph(c(1, 2, 2, 3), directed = FALSE)
-  E(g)$weight <- c(1, 2)
-  E(g)$foo <- c("a", "b")
-  g
-}
+# The `simple_graph_with_edge_attrs()` fixture used below lives in
+# helper-test-functions.R.
 
 test_that("simplify() applies edge.attr.comb to an already-simple graph", {
   # `edge.attr.comb` does not only combine attributes across merged edges, it
@@ -1424,24 +1415,27 @@ test_that("simplify() applies edge.attr.comb to an already-simple graph", {
   # simple still has to go through the combination.
 
   # The default list ends in "ignore", so `weight` survives and `foo` does not.
-  expect_equal(edge_attr_names(simplify(simple_graph_with_attrs())), "weight")
+  expect_equal(
+    edge_attr_names(simplify(simple_graph_with_edge_attrs())),
+    "weight"
+  )
   expect_length(
     edge_attr_names(simplify(
-      simple_graph_with_attrs(),
+      simple_graph_with_edge_attrs(),
       edge.attr.comb = "ignore"
     )),
     0
   )
   expect_setequal(
     edge_attr_names(simplify(
-      simple_graph_with_attrs(),
+      simple_graph_with_edge_attrs(),
       edge.attr.comb = list(weight = "sum", foo = "first")
     )),
     c("weight", "foo")
   )
 
   # Values are untouched -- each edge is its own group.
-  expect_equal(E(simplify(simple_graph_with_attrs()))$weight, c(1, 2))
+  expect_equal(E(simplify(simple_graph_with_edge_attrs()))$weight, c(1, 2))
 })
 
 test_that("simplify() is still cache-sensitive, which is a C-core issue", {
@@ -1455,8 +1449,8 @@ test_that("simplify() is still cache-sensitive, which is a C-core issue", {
   # `is_simple(graph)`, which warmed the cache on every call and made the
   # cache-warm answer the only answer. It cannot cure it either --
   # that fix belongs in src/vendor/cigraph/src/operators/simplify.c.
-  cold <- simple_graph_with_attrs()
-  warm <- simple_graph_with_attrs()
+  cold <- simple_graph_with_edge_attrs()
+  warm <- simple_graph_with_edge_attrs()
   invisible(is_simple(warm))
 
   expect_length(edge_attr_names(simplify(cold, edge.attr.comb = "ignore")), 0)
diff --git a/tests/testthat/test-other.R b/tests/testthat/test-other.R
index 8e6111d5123..bd9cf14ecde 100644
--- a/tests/testthat/test-other.R
+++ b/tests/testthat/test-other.R
@@ -63,19 +63,20 @@ test_that("serialization works", {
   })
 })
 
-# The old-format `karate_oldstyle` fixture (and its `karate_oldstyle_names`)
-# used below live in helper-test-functions.R.
+# The old-format `karate_oldstyle_graph()` fixture,
+# and its `karate_oldstyle_vertex_names()`,
+# live in helper-test-functions.R.
 
 test_that("VS/ES require explicit conversion", {
   expect_snapshot_igraph_error({
-    V(karate_oldstyle)
+    V(karate_oldstyle_graph())
   })
 })
 
 test_that("VS/ES work with old data type", {
-  karate2 <- upgrade_graph(karate_oldstyle)
+  karate2 <- upgrade_graph(karate_oldstyle_graph())
   vs2 <- V(karate2)
 
   expect_length(vs2, 34)
-  expect_equal(vs2$name, karate_oldstyle_names)
+  expect_equal(vs2$name, karate_oldstyle_vertex_names())
 })