diff --git a/R/data_frame.R b/R/data_frame.R
index 9568b631b1..feae33642c 100644
--- a/R/data_frame.R
+++ b/R/data_frame.R
@@ -100,16 +100,17 @@ graph.data.frame <- function(d, directed = TRUE, vertices = NULL) { # nocov star
 #' is returned, in a list with named entries `vertices` and `edges`.
 #'
 #' @param d A data frame containing a symbolic edge list in the first two
-#'   columns. Additional columns are considered as edge attributes.  Since
+#'   columns, as vertex names or vertex IDs.
+#    Additional columns are considered as edge attributes.  Since
 #'   version 0.7 this argument is coerced to a data frame with
-#'   `as.data.frame`.
+#'   [as.data.frame()].
 #' @param directed Logical scalar, whether or not to create a directed graph.
 #' @param vertices A data frame with vertex metadata, or `NULL`. See
 #'   details below. Since version 0.7 this argument is coerced to a data frame
-#'   with `as.data.frame`, if not `NULL`.
+#'   with [as.data.frame()], if not `NULL`.
 #' @return An igraph graph object for `graph_from_data_frame()`, and either a
 #'   data frame or a list of two data frames named `edges` and
-#'   `vertices` for `as.data.frame`.
+#'   `vertices` for [as.data.frame()].
 #' @note For `graph_from_data_frame()` `NA` elements in the first two
 #' columns \sQuote{d} are replaced by the string \dQuote{NA} before creating
 #' the graph. This means that all `NA`s will correspond to a single
@@ -155,37 +156,61 @@ graph.data.frame <- function(d, directed = TRUE, vertices = NULL) { # nocov star
 #' @export
 graph_from_data_frame <- function(d, directed = TRUE, vertices = NULL) {
   d <- as.data.frame(d)
-  if (!is.null(vertices)) {
+  if (is.character(vertices) || is.factor(vertices)) {
+    vertices <- data.frame(name = as.character(vertices))
+  } else if (is.matrix(vertices)) {
     vertices <- as.data.frame(vertices)
+  } else if (!is.null(vertices) && !is.data.frame(vertices)) {
+    stop("`vertices` must be a data frame or a character vector if given")
   }
 
   if (ncol(d) < 2) {
-    stop("the data frame should contain at least two columns")
+    stop("`d` should contain at least two columns")
   }
 
-  ## Handle if some elements are 'NA'
-  if (any(is.na(d[, 1:2]))) {
-    warning("In `d' `NA' elements were replaced with string \"NA\"")
-    d[, 1:2][is.na(d[, 1:2])] <- "NA"
-  }
-  if (!is.null(vertices) && any(is.na(vertices[, 1]))) {
-    warning("In `vertices[,1]' `NA' elements were replaced with string \"NA\"")
-    vertices[, 1][is.na(vertices[, 1])] <- "NA"
+  if (!is.null(vertices) && ncol(vertices) >= 1) {
+    names <- vertices$name
+    if (!is.null(names)) {
+      if (anyNA(names)) {
+        warning('Replacing `NA` in vertex names in `vertices` with the string "NA"')
+        names[is.na(names)] <- "NA"
+      }
+      if (anyDuplicated(names)) {
+        stop("Duplicate vertex names")
+      }
+    }
+  } else {
+    names <- NULL
   }
 
-  names <- unique(c(as.character(d[, 1]), as.character(d[, 2])))
-  if (!is.null(vertices)) {
-    names2 <- names
-    vertices <- as.data.frame(vertices)
-    if (ncol(vertices) < 1) {
-      stop("Vertex data frame contains no rows")
+  if (is.numeric(d[[1]]) && !is.factor(d[[1]]) && is.numeric(d[[2]]) && !is.factor(d[[2]])) {
+    edges <- rbind(d[[1]], d[[2]])
+    names <- seq_len(max(edges, 0L))
+  } else {
+    if (is.null(names)) {
+      names <- unique(c(as.character(d[[1]]), as.character(d[[2]])))
+    }
+
+    if (is.null(vertices)) {
+      vertices <- data.frame(name = names)
+    } else if (!("name" %in% names(vertices))) {
+      vertices <- cbind(data.frame(name = names), vertices)
     }
-    names <- as.character(vertices[, 1])
-    if (any(duplicated(names))) {
-      stop("Duplicate vertex names")
+
+    name_edges <- rbind(as.character(d[[1]]), as.character(d[[2]]))
+
+    if (anyNA(name_edges)) {
+      warning('Replacing `NA` in vertex names in `d` with the string "NA"')
+      name_edges[is.na(name_edges)] <- "NA"
     }
-    if (any(!names2 %in% names)) {
-      stop("Some vertex names in edge list are not listed in vertex data frame")
+
+    edges <- matrix(match(name_edges, names), nrow = 2)
+    if (anyNA(edges)) {
+      stop(
+        "Vertex name ",
+        name_edges[is.na(edges)][[1]],
+        " in edge list is not listed in vertex data frame"
+      )
     }
   }
 
@@ -193,44 +218,28 @@ graph_from_data_frame <- function(d, directed = TRUE, vertices = NULL) {
   g <- make_empty_graph(n = 0, directed = directed)
 
   # vertex attributes
-  attrs <- list(name = names)
-  if (!is.null(vertices)) {
-    if (ncol(vertices) > 1) {
-      for (i in 2:ncol(vertices)) {
-        newval <- vertices[, i]
-        if (inherits(newval, "factor")) {
-          newval <- as.character(newval)
-        }
-        attrs[[names(vertices)[i]]] <- newval
-      }
-    }
-  }
+  vattrs <- lapply(vertices, unfactor)
 
   # add vertices
-  g <- add_vertices(g, length(names), attr = attrs)
-
-  # create edge list
-  from <- as.character(d[, 1])
-  to <- as.character(d[, 2])
-  edges <- rbind(match(from, names), match(to, names))
+  g <- add_vertices(g, length(names), attr = vattrs)
 
   # edge attributes
-  attrs <- list()
-  if (ncol(d) > 2) {
-    for (i in 3:ncol(d)) {
-      newval <- d[, i]
-      if (inherits(newval, "factor")) {
-        newval <- as.character(newval)
-      }
-      attrs[[names(d)[i]]] <- newval
-    }
-  }
+  eattrs <- lapply(d[-1:-2], unfactor)
 
   # add the edges
-  g <- add_edges(g, edges, attr = attrs)
+  g <- add_edges(g, edges, attr = eattrs)
+
   g
 }
 
+unfactor <- function(x) {
+  if (!inherits(x, "factor")) {
+    return(x)
+  }
+
+  as.character(x)
+}
+
 #' @rdname graph_from_data_frame
 #' @param ... Passed to `graph_from_data_frame()`.
 #' @export
diff --git a/man/graph.data.frame.Rd b/man/graph.data.frame.Rd
index 3edbba9ce8..3f641e2ea7 100644
--- a/man/graph.data.frame.Rd
+++ b/man/graph.data.frame.Rd
@@ -8,15 +8,15 @@ graph.data.frame(d, directed = TRUE, vertices = NULL)
 }
 \arguments{
 \item{d}{A data frame containing a symbolic edge list in the first two
-columns. Additional columns are considered as edge attributes.  Since
+columns, as vertex names or vertex IDs.
 version 0.7 this argument is coerced to a data frame with
-\code{as.data.frame}.}
+\code{\link[=as.data.frame]{as.data.frame()}}.}
 
 \item{directed}{Logical scalar, whether or not to create a directed graph.}
 
 \item{vertices}{A data frame with vertex metadata, or \code{NULL}. See
 details below. Since version 0.7 this argument is coerced to a data frame
-with \code{as.data.frame}, if not \code{NULL}.}
+with \code{\link[=as.data.frame]{as.data.frame()}}, if not \code{NULL}.}
 }
 \description{
 \ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#deprecated}{\figure{lifecycle-deprecated.svg}{options: alt='[Deprecated]'}}}{\strong{[Deprecated]}}
diff --git a/man/graph_from_data_frame.Rd b/man/graph_from_data_frame.Rd
index afcbdd549a..6bd5901855 100644
--- a/man/graph_from_data_frame.Rd
+++ b/man/graph_from_data_frame.Rd
@@ -19,22 +19,22 @@ from_data_frame(...)
 edges, or both. The default is \sQuote{edges}.}
 
 \item{d}{A data frame containing a symbolic edge list in the first two
-columns. Additional columns are considered as edge attributes.  Since
+columns, as vertex names or vertex IDs.
 version 0.7 this argument is coerced to a data frame with
-\code{as.data.frame}.}
+\code{\link[=as.data.frame]{as.data.frame()}}.}
 
 \item{directed}{Logical scalar, whether or not to create a directed graph.}
 
 \item{vertices}{A data frame with vertex metadata, or \code{NULL}. See
 details below. Since version 0.7 this argument is coerced to a data frame
-with \code{as.data.frame}, if not \code{NULL}.}
+with \code{\link[=as.data.frame]{as.data.frame()}}, if not \code{NULL}.}
 
 \item{...}{Passed to \code{graph_from_data_frame()}.}
 }
 \value{
 An igraph graph object for \code{graph_from_data_frame()}, and either a
 data frame or a list of two data frames named \code{edges} and
-\code{vertices} for \code{as.data.frame}.
+\code{vertices} for \code{\link[=as.data.frame]{as.data.frame()}}.
 }
 \description{
 This function creates an igraph graph from one or two data frames containing
diff --git a/tests/testthat/test-betweenness.R b/tests/testthat/test-betweenness.R
index 9b3fc11e91..3d480ea3f0 100644
--- a/tests/testthat/test-betweenness.R
+++ b/tests/testthat/test-betweenness.R
@@ -94,5 +94,5 @@ test_that("shortest paths are compared with tolerance when calculating betweenne
   g <- graph_from_data_frame(edges, directed = FALSE)
   result <- betweenness(g, weights = edges.dists)
 
-  expect_that(result[1:5], equals(c("1" = 0, "2" = 44, "3" = 71, "4" = 36.5, "6" = 44)))
+  expect_that(result[c(1:4, 6)], equals(c(0, 44, 71, 36.5, 44)))
 })
diff --git a/tests/testthat/test-get.shortest.paths.R b/tests/testthat/test-get.shortest.paths.R
index b4406bac2d..dc0b04b6c6 100644
--- a/tests/testthat/test-get.shortest.paths.R
+++ b/tests/testthat/test-get.shortest.paths.R
@@ -18,7 +18,7 @@ test_that("shortest_paths works", {
   edges <- as.data.frame(edges)
   edges[[3]] <- as.numeric(as.character(edges[[3]]))
 
-  g <- graph_from_data_frame(as.data.frame(edges))
+  g <- graph_from_data_frame(edges)
 
   all1 <- all_shortest_paths(g, "s", "t", weights = NA)$vpaths
 
diff --git a/tests/testthat/test-graph.data.frame.R b/tests/testthat/test-graph.data.frame.R
index ada18f0aba..cba1e065fd 100644
--- a/tests/testthat/test-graph.data.frame.R
+++ b/tests/testthat/test-graph.data.frame.R
@@ -40,7 +40,6 @@ test_that("graph_from_data_frame() creates attributes for zero-row data frames (
 test_that("graph_from_data_frame works on matrices", {
   el <- cbind(1:5, 5:1, weight = 1:5)
   g <- graph_from_data_frame(el)
-  g <- delete_vertex_attr(g, "name")
   el2 <- as_data_frame(g)
   expect_that(as.data.frame(el), is_equivalent_to(el2))
 })
diff --git a/tests/testthat/test-graph.maxflow.R b/tests/testthat/test-graph.maxflow.R
index b7264a5396..e130468b9d 100644
--- a/tests/testthat/test-graph.maxflow.R
+++ b/tests/testthat/test-graph.maxflow.R
@@ -1,11 +1,18 @@
 test_that("max_flow works", {
-  E <- rbind(c(1, 3, 3), c(3, 4, 1), c(4, 2, 2), c(1, 5, 1), c(5, 6, 2), c(6, 2, 10))
+  E <- rbind(
+    c(1, 3, 3),
+    c(3, 4, 1),
+    c(4, 2, 2),
+    c(1, 5, 1),
+    c(5, 6, 2),
+    c(6, 2, 10)
+  )
   colnames(E) <- c("from", "to", "capacity")
   g1 <- graph_from_data_frame(as.data.frame(E))
-  fl <- max_flow(g1, source = "1", target = "2")
+  fl <- max_flow(g1, source = 1, target = 2)
   expect_that(fl$value, equals(2))
   expect_that(as.vector(fl$flow), equals(rep(1, 6)))
   expect_that(sort(as.vector(fl$cut)), equals(c(2, 4)))
-  expect_that(sort(as.vector(fl$partition1)), equals(1:2))
-  expect_that(sort(as.vector(fl$partition2)), equals(3:6))
+  expect_that(sort(as.vector(fl$partition1)), equals(c(1, 3)))
+  expect_that(sort(as.vector(fl$partition2)), equals(c(2, 4, 5, 6)))
 })