diff --git a/NAMESPACE b/NAMESPACE
index 19c88795d6..f0cc95bf2c 100644
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -937,6 +937,7 @@ importFrom(rlang,"%||%")
 importFrom(rlang,.data)
 importFrom(rlang,.env)
 importFrom(rlang,as_function)
+importFrom(rlang,caller_env)
 importFrom(rlang,check_dots_empty)
 importFrom(rlang,check_installed)
 importFrom(rlang,global_env)
diff --git a/R/adjacency.R b/R/adjacency.R
index 9ebf52700c..84ded07597 100644
--- a/R/adjacency.R
+++ b/R/adjacency.R
@@ -228,6 +228,7 @@ graph_from_adjacency_matrix <- function(adjmatrix,
                                         ),
                                         weighted = NULL, diag = TRUE,
                                         add.colnames = NULL, add.rownames = NA) {
+  ensure_no_na(adjmatrix, "adjacency matrix")
   mode <- igraph.match.arg(mode)
 
   if (!is.matrix(adjmatrix) && !inherits(adjmatrix, "Matrix")) {
diff --git a/R/conversion.R b/R/conversion.R
index b68a3975df..839afc1616 100644
--- a/R/conversion.R
+++ b/R/conversion.R
@@ -1397,10 +1397,8 @@ graph_from_data_frame <- function(d, directed = TRUE, vertices = NULL) {
   }
 
   ## Handle if some elements are 'NA'
-  if (any(is.na(d[, 1:2]))) {
-    cli::cli_warn("In {.code d}, {.code NA} elements were replaced with string {.str NA}.")
-    d[, 1:2][is.na(d[, 1:2])] <- "NA"
-  }
+  ensure_no_na(d, "edge data frame")
+
   if (!is.null(vertices) && any(is.na(vertices[, 1]))) {
     cli::cli_warn("In {.code vertices[,1]}, {.code NA} elements were replaced with string {.str NA}.")
     vertices[, 1][is.na(vertices[, 1])] <- "NA"
@@ -1489,8 +1487,9 @@ from_data_frame <- function(...) constructor_spec(graph_from_data_frame, ...)
 #' graph_from_edgelist(cbind(1:10, c(2:10, 1)))
 graph_from_edgelist <- function(el, directed = TRUE) {
   if (!is.matrix(el) || ncol(el) != 2) {
-    cli::cli_abort("graph_from_edgelist expects a matrix with two columns")
+    cli::cli_abort("graph_from_edgelist expects a matrix with two columns.")
   }
+  ensure_no_na(el, "edgelist")
 
   if (nrow(el) == 0) {
     res <- make_empty_graph(directed = directed)
diff --git a/R/incidence.R b/R/incidence.R
index dd1118b735..9a3c90010a 100644
--- a/R/incidence.R
+++ b/R/incidence.R
@@ -168,6 +168,7 @@ graph_from_biadjacency_matrix <- function(incidence, directed = FALSE,
                                           multiple = FALSE, weighted = NULL,
                                           add.names = NULL) {
   # Argument checks
+  ensure_no_na(incidence, "biadjacency matrix")
   directed <- as.logical(directed)
   mode <- igraph.match.arg(mode)
 
diff --git a/R/utils-assert-args.R b/R/utils-assert-args.R
index 3bb7d16736..e66cd3b31d 100644
--- a/R/utils-assert-args.R
+++ b/R/utils-assert-args.R
@@ -32,3 +32,10 @@ igraph.match.arg <- function(arg, values, error_call = rlang::caller_env()) {
     error_call = error_call
   )
 }
+
+#' @importFrom rlang caller_env
+ensure_no_na <- function(x, what, call = caller_env()) {
+  if (any(is.na(x))) {
+    cli::cli_abort("Cannot create a graph object because the {what} contains NAs.", call = call)
+  }
+}
diff --git a/tests/testthat/_snaps/adjacency.md b/tests/testthat/_snaps/adjacency.md
index c46c414628..1af5c9cbce 100644
--- a/tests/testthat/_snaps/adjacency.md
+++ b/tests/testthat/_snaps/adjacency.md
@@ -139,3 +139,11 @@
       IGRAPH U--- 2 0 -- 
       + edges:
 
+# graph_from_adjacency_matrix errors for NAs
+
+    Code
+      graph_from_adjacency_matrix(A)
+    Condition
+      Error in `graph_from_adjacency_matrix()`:
+      ! Cannot create a graph object because the adjacency matrix contains NAs.
+
diff --git a/tests/testthat/_snaps/conversion.md b/tests/testthat/_snaps/conversion.md
index 8da10b7890..33624b7d48 100644
--- a/tests/testthat/_snaps/conversion.md
+++ b/tests/testthat/_snaps/conversion.md
@@ -87,3 +87,11 @@
       2    2  3    2         b          B       c        C
       3    1  3    1         a          A       c        C
 
+# graph_from_edgelist errors for NAs
+
+    Code
+      graph_from_edgelist(A)
+    Condition
+      Error:
+      ! Cannot create a graph object because the edgelist contains NAs.
+
diff --git a/tests/testthat/_snaps/incidence.md b/tests/testthat/_snaps/incidence.md
index 2b9e6ff16a..dbb1ba9a91 100644
--- a/tests/testthat/_snaps/incidence.md
+++ b/tests/testthat/_snaps/incidence.md
@@ -85,3 +85,11 @@
       ! `multiple` and `weighted` cannot be both `TRUE`.
       igraph either interprets numbers larger than 1 as weights or as multiplicities, but it cannot be both.
 
+# graph_from_biadjacency_matrix errors for NAs
+
+    Code
+      graph_from_biadjacency_matrix(A)
+    Condition
+      Error in `graph_from_biadjacency_matrix()`:
+      ! Cannot create a graph object because the biadjacency matrix contains NAs.
+
diff --git a/tests/testthat/test-adjacency.R b/tests/testthat/test-adjacency.R
index 2e9983b99f..0812b24973 100644
--- a/tests/testthat/test-adjacency.R
+++ b/tests/testthat/test-adjacency.R
@@ -670,7 +670,6 @@ test_that("sparse/dense matrices no loops works", {
   g <- graph_from_adjacency_matrix(A, diag = FALSE)
   expect_ecount(g, 1)
   expect_equal(get_edge_ids(g, c(1, 2)), 1)
-
 })
 
 test_that("sparse/dense matrices multiple works", {
@@ -681,11 +680,10 @@ test_that("sparse/dense matrices multiple works", {
   expect_ecount(g, 3)
   expect_equal(as_edgelist(g), matrix(c(1, 2), 3, 2, byrow = TRUE))
 
-  A <- as(A,"dgCMatrix")
+  A <- as(A, "dgCMatrix")
   g <- graph_from_adjacency_matrix(A, diag = FALSE)
   expect_ecount(g, 3)
   expect_equal(as_edgelist(g), matrix(c(1, 2), 3, 2, byrow = TRUE))
-
 })
 
 test_that("sparse/dense matrices min/max/plus", {
@@ -712,3 +710,8 @@ test_that("sparse/dense matrices min/max/plus", {
   g <- graph_from_adjacency_matrix(A, diag = FALSE, mode = "plus", weighted = TRUE)
   expect_equal(E(g)$weight[1], 5)
 })
+
+test_that("graph_from_adjacency_matrix errors for NAs", {
+  A <- matrix(c(1, 1, NA, 1), 2, 2)
+  expect_snapshot(graph_from_adjacency_matrix(A), error = TRUE)
+})
diff --git a/tests/testthat/test-conversion.R b/tests/testthat/test-conversion.R
index bf8f5e97b6..b097db125f 100644
--- a/tests/testthat/test-conversion.R
+++ b/tests/testthat/test-conversion.R
@@ -597,6 +597,9 @@ test_that("edge names work", {
   )
 })
 
+test_that("graph_from_edgelist errors for NAs", {
+  A <- matrix(c(1, 2, NA, 1), 2, 2)
+  expect_snapshot(graph_from_edgelist(A), error = TRUE)
 test_that("graph_from_data_frame works with factors", {
   actors <- data.frame(
     name = c("Alice", "Bob", "Cecil", "David", "Esmeralda"),
diff --git a/tests/testthat/test-incidence.R b/tests/testthat/test-incidence.R
index 47034a9deb..9966a8986c 100644
--- a/tests/testthat/test-incidence.R
+++ b/tests/testthat/test-incidence.R
@@ -175,3 +175,8 @@ test_that("graph_from_biadjacency_matrix() errors well", {
     (g <- graph_from_biadjacency_matrix(inc, multiple = TRUE, weighted = TRUE))
   })
 })
+
+test_that("graph_from_biadjacency_matrix errors for NAs", {
+  A <- matrix(c(1, 1, NA, 1), 2, 2)
+  expect_snapshot(graph_from_biadjacency_matrix(A), error = TRUE)
+})