diff --git a/R/cycles.R b/R/cycles.R
index c3d65b5cae0..4d6c1d8d4b2 100644
--- a/R/cycles.R
+++ b/R/cycles.R
@@ -31,6 +31,7 @@
 #' a specific cycle.
 #'
 #' @param graph The input graph.
+#' @inheritParams rlang::args_dots_empty
 #' @param mode Character constant specifying how to handle directed graphs.
 #'   `out` follows edge directions, `in` follows edges in the reverse direction,
 #'   and `all` ignores edge directions. Ignored in undirected graphs.
@@ -49,7 +50,33 @@
 #' @family cycles
 #' @export
 
-find_cycle <- function(graph, mode = c("out", "in", "all", "total")) {
+find_cycle <- function(
+  graph,
+  ...,
+  mode = c("out", "in", "all", "total")
+) {
+  # BEGIN GENERATED ARG_HANDLE: find_cycle, do not edit, see tools/generate-migrations.R
+  if (...length() > 0L) {
+    .arg_handle <- migrate_recover_args(
+      list(...),
+      current = list(mode = mode),
+      recover_new = c("mode"),
+      recover_old = c("mode"),
+      match_names = c("mode"),
+      match_to = c("mode"),
+      defaults = list(mode = c("out", "in", "all", "total")),
+      head_args = c("graph"),
+      fn_name = "find_cycle"
+    )
+    list2env(.arg_handle$values, environment())
+    lifecycle::deprecate_soft(
+      "3.0.0",
+      what = I(.arg_handle$what),
+      details = .arg_handle$details
+    )
+  }
+  # END GENERATED ARG_HANDLE
+
   find_cycle_impl(
     graph = graph,
     mode = mode
diff --git a/R/random_walk.R b/R/random_walk.R
index d6252a56838..4d610ccecaa 100644
--- a/R/random_walk.R
+++ b/R/random_walk.R
@@ -16,6 +16,7 @@
 #' @param graph The input graph, might be undirected or directed.
 #' @param start The start vertex.
 #' @param steps The number of steps to make.
+#' @inheritParams rlang::args_dots_empty
 #' @param weights The edge weights. Larger edge weights increase the
 #'   probability that an edge is selected by the random walker. In other
 #'   words, larger edge weights correspond to stronger connections. The
@@ -51,10 +52,37 @@ random_walk <- function(
   graph,
   start,
   steps,
+  ...,
   weights = NULL,
   mode = c("out", "in", "all", "total"),
   stuck = c("return", "error")
 ) {
+  # BEGIN GENERATED ARG_HANDLE: random_walk, do not edit, see tools/generate-migrations.R
+  if (...length() > 0L) {
+    .arg_handle <- migrate_recover_args(
+      list(...),
+      current = list(weights = weights, mode = mode, stuck = stuck),
+      recover_new = c("weights", "mode", "stuck"),
+      recover_old = c("weights", "mode", "stuck"),
+      match_names = c("weights", "mode", "stuck"),
+      match_to = c("weights", "mode", "stuck"),
+      defaults = list(
+        weights = NULL,
+        mode = c("out", "in", "all", "total"),
+        stuck = c("return", "error")
+      ),
+      head_args = c("graph", "start", "steps"),
+      fn_name = "random_walk"
+    )
+    list2env(.arg_handle$values, environment())
+    lifecycle::deprecate_soft(
+      "3.0.0",
+      what = I(.arg_handle$what),
+      details = .arg_handle$details
+    )
+  }
+  # END GENERATED ARG_HANDLE
+
   mode <- match.arg(mode)
   stuck <- match.arg(stuck)
   out <- random_walk_impl(
@@ -71,15 +99,43 @@ random_walk <- function(
 }
 
 #' @rdname random_walk
+#' @inheritParams rlang::args_dots_empty
 #' @export
 random_edge_walk <- function(
   graph,
   start,
   steps,
+  ...,
   weights = NULL,
   mode = c("out", "in", "all", "total"),
   stuck = c("return", "error")
 ) {
+  # BEGIN GENERATED ARG_HANDLE: random_edge_walk, do not edit, see tools/generate-migrations.R
+  if (...length() > 0L) {
+    .arg_handle <- migrate_recover_args(
+      list(...),
+      current = list(weights = weights, mode = mode, stuck = stuck),
+      recover_new = c("weights", "mode", "stuck"),
+      recover_old = c("weights", "mode", "stuck"),
+      match_names = c("weights", "mode", "stuck"),
+      match_to = c("weights", "mode", "stuck"),
+      defaults = list(
+        weights = NULL,
+        mode = c("out", "in", "all", "total"),
+        stuck = c("return", "error")
+      ),
+      head_args = c("graph", "start", "steps"),
+      fn_name = "random_edge_walk"
+    )
+    list2env(.arg_handle$values, environment())
+    lifecycle::deprecate_soft(
+      "3.0.0",
+      what = I(.arg_handle$what),
+      details = .arg_handle$details
+    )
+  }
+  # END GENERATED ARG_HANDLE
+
   mode <- match.arg(mode)
   stuck <- match.arg(stuck)
   out <- random_walk_impl(
diff --git a/man/find_cycle.Rd b/man/find_cycle.Rd
index c76504fa175..f35f567bc46 100644
--- a/man/find_cycle.Rd
+++ b/man/find_cycle.Rd
@@ -4,11 +4,13 @@
 \alias{find_cycle}
 \title{Finds a cycle in a graph, if there is one}
 \usage{
-find_cycle(graph, mode = c("out", "in", "all", "total"))
+find_cycle(graph, ..., mode = c("out", "in", "all", "total"))
 }
 \arguments{
 \item{graph}{The input graph.}
 
+\item{...}{These dots are for future extensions and must be empty.}
+
 \item{mode}{Character constant specifying how to handle directed graphs.
 \code{out} follows edge directions, \verb{in} follows edges in the reverse direction,
 and \code{all} ignores edge directions. Ignored in undirected graphs.}
diff --git a/man/random_walk.Rd b/man/random_walk.Rd
index 5232e145b23..2b4887a6fa5 100644
--- a/man/random_walk.Rd
+++ b/man/random_walk.Rd
@@ -9,6 +9,7 @@ random_walk(
   graph,
   start,
   steps,
+  ...,
   weights = NULL,
   mode = c("out", "in", "all", "total"),
   stuck = c("return", "error")
@@ -18,6 +19,7 @@ random_edge_walk(
   graph,
   start,
   steps,
+  ...,
   weights = NULL,
   mode = c("out", "in", "all", "total"),
   stuck = c("return", "error")
@@ -30,6 +32,8 @@ random_edge_walk(
 
 \item{steps}{The number of steps to make.}
 
+\item{...}{These dots are for future extensions and must be empty.}
+
 \item{weights}{The edge weights. Larger edge weights increase the
 probability that an edge is selected by the random walker. In other
 words, larger edge weights correspond to stronger connections. The
diff --git a/tests/testthat/test-cycles.R b/tests/testthat/test-cycles.R
index 383a9a3a885..27b32c6de73 100644
--- a/tests/testthat/test-cycles.R
+++ b/tests/testthat/test-cycles.R
@@ -111,3 +111,24 @@ test_that("simple_cycles_callback handles errors in callback", {
     "Error in R callback function"
   )
 })
+
+# ---- ellipsis migration: argument coverage ----------------------------
+
+test_that("find_cycle mode variants distinguish edge orientation", {
+  # A directed acyclic triangle is only cyclic when directions are ignored.
+  g <- make_graph(c(1, 2, 1, 3, 2, 3), directed = TRUE)
+
+  expect_length(find_cycle(g)$vertices, 0)
+  expect_length(find_cycle(g, mode = "in")$vertices, 0)
+
+  cyc <- find_cycle(g, mode = "all")
+  expect_length(cyc$vertices, 3)
+  expect_length(cyc$edges, 3)
+})
+
+test_that("find_cycle recovers legacy positional arguments", {
+  g <- make_graph(c(1, 2, 1, 3, 2, 3), directed = TRUE)
+  lifecycle::expect_deprecated(res <- find_cycle(g, "all"))
+  expect_equal(res, find_cycle(g, mode = "all"))
+  expect_length(res$vertices, 3)
+})
diff --git a/tests/testthat/test-random_walk.R b/tests/testthat/test-random_walk.R
index f419810e3dd..1322de9d886 100644
--- a/tests/testthat/test-random_walk.R
+++ b/tests/testthat/test-random_walk.R
@@ -79,3 +79,52 @@ test_that("directed random_edge_walk can return wtih an error when stuck", {
     "Random walk got stuck"
   )
 })
+
+# ---- ellipsis migration: argument coverage ----------------------------
+
+test_that("random_walk follows edge weights and returns partial walks when stuck", {
+  igraph_local_seed(42)
+
+  # The heavy edge to vertex 4 forces the walk to bounce between 1 and 4.
+  g <- make_star(5, mode = "undirected")
+  w <- random_walk(g, start = 1, steps = 6, weights = c(1, 1, 1e12, 1))
+  expect_equal(as_ids(w), rep_len(c(1, 4), 7))
+
+  # A walk starting on a sink vertex stops immediately with stuck = "return".
+  g2 <- make_star(11, mode = "out")
+  w2 <- random_walk(g2, start = 7, steps = 10, stuck = "return")
+  expect_equal(as_ids(w2), 7)
+})
+
+test_that("random_walk recovers legacy positional arguments", {
+  g <- make_star(5, mode = "undirected")
+  lifecycle::expect_deprecated(
+    res <- igraph_with_seed(42, random_walk(g, 1, 6, c(1, 1, 1e12, 1)))
+  )
+  expect_equal(
+    res,
+    igraph_with_seed(42, random_walk(g, 1, 6, weights = c(1, 1, 1e12, 1)))
+  )
+  expect_equal(as_ids(res), rep_len(c(1, 4), 7))
+})
+
+test_that("random_edge_walk follows edge weights", {
+  igraph_local_seed(42)
+  # A two-cycle with one heavy edge keeps the walker crossing that edge.
+  g <- make_ring(2)
+  w <- random_edge_walk(g, start = 1, steps = 8, weights = c(1e12, 1))
+  expect_length(w, 8)
+  expect_equal(as.integer(w), rep(1L, 8))
+})
+
+test_that("random_edge_walk recovers legacy positional arguments", {
+  g <- make_ring(2)
+  lifecycle::expect_deprecated(
+    res <- igraph_with_seed(42, random_edge_walk(g, 1, 8, c(1e12, 1)))
+  )
+  expect_equal(
+    res,
+    igraph_with_seed(42, random_edge_walk(g, 1, 8, weights = c(1e12, 1)))
+  )
+  expect_equal(as.integer(res), rep(1L, 8))
+})
diff --git a/tools/migrations/walks-cycles.R b/tools/migrations/walks-cycles.R
new file mode 100644
index 00000000000..88056db8061
--- /dev/null
+++ b/tools/migrations/walks-cycles.R
@@ -0,0 +1,43 @@
+# Argument-signature migrations: walks-cycles
+# Schema: see tools/migrations/README.md. Regenerate with:
+#   Rscript tools/generate-migrations.R
+
+migrations <- list(
+  find_cycle = list(
+    old = function(graph, mode) {},
+    new = function(
+      graph,
+      ...,
+      mode = c("out", "in", "all", "total")
+    ) {},
+    when = "3.0.0"
+  ),
+
+  random_edge_walk = list(
+    old = function(graph, start, steps, weights, mode, stuck) {},
+    new = function(
+      graph,
+      start,
+      steps,
+      ...,
+      weights = NULL,
+      mode = c("out", "in", "all", "total"),
+      stuck = c("return", "error")
+    ) {},
+    when = "3.0.0"
+  ),
+
+  random_walk = list(
+    old = function(graph, start, steps, weights, mode, stuck) {},
+    new = function(
+      graph,
+      start,
+      steps,
+      ...,
+      weights = NULL,
+      mode = c("out", "in", "all", "total"),
+      stuck = c("return", "error")
+    ) {},
+    when = "3.0.0"
+  )
+)