diff --git a/tests/testthat/_snaps/conversion.md b/tests/testthat/_snaps/conversion.md
index 12b0bc0c7fd..ebadf3499b9 100644
--- a/tests/testthat/_snaps/conversion.md
+++ b/tests/testthat/_snaps/conversion.md
@@ -52,3 +52,38 @@
       Error in `get.adjacency.dense()`:
       ! Matrices must be either numeric or logical, and the edge attribute is not
 
+# as_long_data_frame() works correctly with and without names
+
+    Code
+      ring <- make_ring(3)
+      as_long_data_frame(ring)
+    Output
+        from to
+      1    1  2
+      2    2  3
+      3    1  3
+    Code
+      V(ring)$name <- letters[1:3]
+      as_long_data_frame(ring)
+    Output
+        from to from_name to_name
+      1    1  2         a       b
+      2    2  3         b       c
+      3    1  3         a       c
+    Code
+      V(ring)$score <- LETTERS[1:3]
+      as_long_data_frame(ring)
+    Output
+        from to from_name from_score to_name to_score
+      1    1  2         a          A       b        B
+      2    2  3         b          B       c        C
+      3    1  3         a          A       c        C
+    Code
+      E(ring)$info <- 3:1
+      as_long_data_frame(ring)
+    Output
+        from to info from_name from_score to_name to_score
+      1    1  2    3         a          A       b        B
+      2    2  3    2         b          B       c        C
+      3    1  3    1         a          A       c        C
+
diff --git a/tests/testthat/test-conversion.R b/tests/testthat/test-conversion.R
index aa8ca51fe75..fd6a5f31b65 100644
--- a/tests/testthat/test-conversion.R
+++ b/tests/testthat/test-conversion.R
@@ -255,3 +255,151 @@ test_that("as_adjacency_matrix() works -- dense + not both", {
     )
   )
 })
+
+test_that("as_edgelist() works", {
+  g <- sample_gnp(100, 3 / 100)
+  e <- as_edgelist(g)
+  g2 <- make_graph(t(e), n = vcount(g), dir = FALSE)
+  expect_isomorphic(g, g2)
+})
+
+test_that("as_adj_list() works", {
+  g <- sample_gnp(50, 2 / 50)
+  al <- as_adj_list(g)
+  g2 <- graph_from_adj_list(al, mode = "all")
+  expect_isomorphic(g, g2)
+  expect_true(isomorphic(g, g2,
+    vertex.color1 = 1:vcount(g),
+    vertex.color2 = 1:vcount(g2),
+    method = "vf2"
+  ))
+
+  ####
+
+  el <- as_adj_edge_list(g)
+  for (i in 1:vcount(g)) {
+    a <- E(g)[.inc(i)]
+    expect_equal(length(a), length(el[[i]]), ignore_attr = TRUE)
+    expect_equal(sort(el[[i]]), sort(a), ignore_attr = TRUE)
+  }
+
+  g <- sample_gnp(50, 4 / 50, directed = TRUE)
+  el1 <- as_adj_edge_list(g, mode = "out")
+  el2 <- as_adj_edge_list(g, mode = "in")
+  for (i in 1:vcount(g)) {
+    a <- E(g)[.from(i)]
+    expect_equal(length(a), length(el1[[i]]), ignore_attr = TRUE)
+    expect_equal(sort(el1[[i]]), sort(a), ignore_attr = TRUE)
+  }
+  for (i in 1:vcount(g)) {
+    a <- E(g)[.to(i)]
+    expect_equal(length(a), length(el2[[i]]), ignore_attr = TRUE)
+    expect_equal(sort(el2[[i]]), sort(a), ignore_attr = TRUE)
+  }
+})
+
+test_that("graph_from_graphnel() works", {
+  skip_if_not_installed("graph")
+  suppressPackageStartupMessages(library(graph, warn.conflicts = FALSE))
+
+  g <- sample_gnp(100, 5 / 100)
+  N <- as_graphnel(g)
+  g2 <- graph_from_graphnel(N)
+  gi <- graph.isomorphic.vf2(g, g2)
+  expect_true(gi$iso)
+  expect_equal(gi$map12, 1:vcount(g))
+  expect_equal(gi$map21, 1:vcount(g))
+
+  ## Attributes
+
+  V(g)$name <- as.character(vcount(g):1)
+  E(g)$weight <- sample(1:10, ecount(g), replace = TRUE)
+  g$name <- "Foobar"
+
+  N <- as_graphnel(g)
+  g2 <- graph_from_graphnel(N)
+  expect_isomorphic(g, g2)
+  expect_equal(V(g)$name, V(g2)$name)
+
+  A <- as_adjacency_matrix(g, attr = "weight", sparse = FALSE)
+  A2 <- as_adjacency_matrix(g2, attr = "weight", sparse = FALSE)
+  expect_equal(A, A)
+  expect_equal(g$name, g2$name)
+})
+
+test_that("as_graphnel() does not duplicate loop edges", {
+  skip_if_not_installed("graph")
+
+  mat <- matrix(c(1, 0.5, 0.5, 0), nrow = 2)
+  dimnames(mat) <- list(c("A", "B"), c("A", "B"))
+
+  igr <- graph_from_adjacency_matrix(mat, mode = "undirected", weighted = TRUE)
+
+  grNEL <- as_graphnel(igr)
+  expect_equal(graph::edgeL(grNEL)$A$edges, c(1, 2))
+})
+
+
+test_that("as_long_data_frame() works correctly with and without names", {
+  expect_snapshot({
+    ring <- make_ring(3)
+    as_long_data_frame(ring)
+
+    V(ring)$name <- letters[1:3]
+    as_long_data_frame(ring)
+
+    V(ring)$score <- LETTERS[1:3]
+    as_long_data_frame(ring)
+
+    E(ring)$info <- 3:1
+    as_long_data_frame(ring)
+  })
+})
+
+test_that("as_biadjacency_matrix() works -- dense", {
+  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
+  g <- graph_from_biadjacency_matrix(I)
+  I2 <- as_biadjacency_matrix(g)
+  expect_equal(I, I2, ignore_attr = TRUE)
+  expect_identical(rownames(I2), as.character(1:7))
+  expect_identical(colnames(I2), as.character(8:12))
+})
+
+test_that("as_biadjacency_matrix() works -- dense named", {
+  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
+  g <- graph_from_biadjacency_matrix(I)
+  V(g)$name <- letters[1:length(V(g))]
+
+  expect_true(is_named(g))
+
+  I2 <- as_biadjacency_matrix(g)
+  expect_equal(I, I2, ignore_attr = TRUE)
+  expect_identical(rownames(I2), c("a", "b", "c", "d", "e", "f", "g"))
+  expect_identical(colnames(I2), c("h", "i", "j", "k", "l"))
+})
+
+test_that("as_biadjacency_matrix() works -- dense + attribute", {
+  withr::local_seed(42)
+  I <- matrix(sample(0:1, 9, replace = TRUE, prob = c(3, 1)), ncol = 3)
+  g <- graph_from_biadjacency_matrix(I)
+  E(g)$something <- letters[1:ecount(g)]
+
+  I2 <- as_biadjacency_matrix(g, attr = "something")
+  expect_equal(
+    unname(I2),
+    matrix(
+      c("a", "c", "0", "b", "0", "0", "0", "0", "0"),
+      nrow = 3L,
+      ncol = 3L
+    )
+  )
+})
+
+test_that("as_biadjacency_matrix() works -- sparse", {
+  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
+  g <- graph_from_biadjacency_matrix(I)
+  I3 <- as_biadjacency_matrix(g, sparse = TRUE)
+  expect_equal(as.matrix(I3), I, ignore_attr = TRUE)
+  expect_identical(rownames(I3), as.character(1:7))
+  expect_identical(colnames(I3), as.character(8:12))
+})
diff --git a/tests/testthat/test-get.adjlist.R b/tests/testthat/test-get.adjlist.R
deleted file mode 100644
index 7c569726e1a..00000000000
--- a/tests/testthat/test-get.adjlist.R
+++ /dev/null
@@ -1,33 +0,0 @@
-test_that("as_adj_list works", {
-  g <- sample_gnp(50, 2 / 50)
-  al <- as_adj_list(g)
-  g2 <- graph_from_adj_list(al, mode = "all")
-  expect_isomorphic(g, g2)
-  expect_true(graph.isomorphic.vf2(g, g2,
-    vertex.color1 = 1:vcount(g),
-    vertex.color2 = 1:vcount(g2)
-  )$iso)
-
-  ####
-
-  el <- as_adj_edge_list(g)
-  for (i in 1:vcount(g)) {
-    a <- E(g)[.inc(i)]
-    expect_equal(length(a), length(el[[i]]), ignore_attr = TRUE)
-    expect_equal(sort(el[[i]]), sort(a), ignore_attr = TRUE)
-  }
-
-  g <- sample_gnp(50, 4 / 50, directed = TRUE)
-  el1 <- as_adj_edge_list(g, mode = "out")
-  el2 <- as_adj_edge_list(g, mode = "in")
-  for (i in 1:vcount(g)) {
-    a <- E(g)[.from(i)]
-    expect_equal(length(a), length(el1[[i]]), ignore_attr = TRUE)
-    expect_equal(sort(el1[[i]]), sort(a), ignore_attr = TRUE)
-  }
-  for (i in 1:vcount(g)) {
-    a <- E(g)[.to(i)]
-    expect_equal(length(a), length(el2[[i]]), ignore_attr = TRUE)
-    expect_equal(sort(el2[[i]]), sort(a), ignore_attr = TRUE)
-  }
-})
diff --git a/tests/testthat/test-get.edgelist.R b/tests/testthat/test-get.edgelist.R
deleted file mode 100644
index f3e4bae9516..00000000000
--- a/tests/testthat/test-get.edgelist.R
+++ /dev/null
@@ -1,6 +0,0 @@
-test_that("as_edgelist works", {
-  g <- sample_gnp(100, 3 / 100)
-  e <- as_edgelist(g)
-  g2 <- make_graph(t(e), n = vcount(g), dir = FALSE)
-  expect_isomorphic(g, g2)
-})
diff --git a/tests/testthat/test-get.incidence.R b/tests/testthat/test-get.incidence.R
deleted file mode 100644
index a750290c07e..00000000000
--- a/tests/testthat/test-get.incidence.R
+++ /dev/null
@@ -1,30 +0,0 @@
-test_that("as_biadjacency_matrix() works -- dense", {
-  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_biadjacency_matrix(I)
-  I2 <- as_biadjacency_matrix(g)
-  expect_equal(I, I2, ignore_attr = TRUE)
-  expect_identical(rownames(I2), as.character(1:7))
-  expect_identical(colnames(I2), as.character(8:12))
-})
-
-test_that("as_biadjacency_matrix() works -- dense named", {
-  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_biadjacency_matrix(I)
-  V(g)$name <- letters[1:length(V(g))]
-
-  expect_true(is_named(g))
-
-  I2 <- as_biadjacency_matrix(g)
-  expect_equal(I, I2, ignore_attr = TRUE)
-  expect_identical(rownames(I2), c("a", "b", "c", "d", "e", "f", "g"))
-  expect_identical(colnames(I2), c("h", "i", "j", "k", "l"))
-})
-
-test_that("as_biadjacency_matrix() works -- sparse", {
-  I <- matrix(sample(0:1, 35, replace = TRUE, prob = c(3, 1)), ncol = 5)
-  g <- graph_from_biadjacency_matrix(I)
-  I3 <- as_biadjacency_matrix(g, sparse = TRUE)
-  expect_equal(as.matrix(I3), I, ignore_attr = TRUE)
-  expect_identical(rownames(I3), as.character(1:7))
-  expect_identical(colnames(I3), as.character(8:12))
-})
diff --git a/tests/testthat/test-graph.data.frame.R b/tests/testthat/test-graph.data.frame.R
index 89f1e05868c..27a1a74bdc0 100644
--- a/tests/testthat/test-graph.data.frame.R
+++ b/tests/testthat/test-graph.data.frame.R
@@ -44,19 +44,3 @@ test_that("graph_from_data_frame works on matrices", {
   el2 <- as_data_frame(g)
   expect_equal(as.data.frame(el), el2, ignore_attr = TRUE)
 })
-
-test_that("as_long_data_frame() works correctly with and without names", {
-  expect_snapshot({
-    ring <- make_ring(3)
-    as_long_data_frame(ring)
-
-    V(ring)$name <- letters[1:3]
-    as_long_data_frame(ring)
-
-    V(ring)$score <- LETTERS[1:3]
-    as_long_data_frame(ring)
-
-    E(ring)$info <- 3:1
-    as_long_data_frame(ring)
-  })
-})
diff --git a/tests/testthat/test-graphNEL.R b/tests/testthat/test-graphNEL.R
deleted file mode 100644
index 07374b9340a..00000000000
--- a/tests/testthat/test-graphNEL.R
+++ /dev/null
@@ -1,41 +0,0 @@
-test_that("graphNEL conversion works", {
-  skip_if_not_installed("graph")
-
-  suppressPackageStartupMessages(library(graph, warn.conflicts = FALSE))
-
-  g <- sample_gnp(100, 5 / 100)
-  N <- as_graphnel(g)
-  g2 <- graph_from_graphnel(N)
-  gi <- graph.isomorphic.vf2(g, g2)
-  expect_true(gi$iso)
-  expect_equal(gi$map12, 1:vcount(g))
-  expect_equal(gi$map21, 1:vcount(g))
-
-  ## Attributes
-
-  V(g)$name <- as.character(vcount(g):1)
-  E(g)$weight <- sample(1:10, ecount(g), replace = TRUE)
-  g$name <- "Foobar"
-
-  N <- as_graphnel(g)
-  g2 <- graph_from_graphnel(N)
-  expect_isomorphic(g, g2)
-  expect_equal(V(g)$name, V(g2)$name)
-
-  A <- as_adjacency_matrix(g, attr = "weight", sparse = FALSE)
-  A2 <- as_adjacency_matrix(g2, attr = "weight", sparse = FALSE)
-  expect_equal(A, A)
-  expect_equal(g$name, g2$name)
-})
-
-test_that("graphNEL does not duplicate loop edges", {
-  skip_if_not_installed("graph")
-
-  mat <- matrix(c(1, 0.5, 0.5, 0), nrow = 2)
-  dimnames(mat) <- list(c("A", "B"), c("A", "B"))
-
-  igr <- graph_from_adjacency_matrix(mat, mode = "undirected", weighted = T)
-
-  grNEL <- as_graphnel(igr)
-  expect_equal(graph::edgeL(grNEL)$A$edges, c(1, 2))
-})