diff --git a/pytools/graph.py b/pytools/graph.py
index 2dbb09f256ee63cbe54e6ba442612479cbfb85c8..7f227bc61715a0674626b37593dbd037ecbca5ad 100644
--- a/pytools/graph.py
+++ b/pytools/graph.py
@@ -38,6 +38,7 @@ Graph Algorithms
 .. autofunction:: contains_cycle
 .. autofunction:: compute_induced_subgraph
 .. autofunction:: validate_graph
+.. autofunction:: is_connected
 
 Type Variables Used
 -------------------
@@ -420,4 +421,40 @@ def validate_graph(graph: Mapping[T, Collection[T]]) -> None:
 
 # }}}
 
+
+# {{{
+
+def is_connected(graph: Mapping[T, Collection[T]]) -> bool:
+    """
+    Returns whether all nodes in *graph* are connected, ignoring
+    the edge direction.
+
+    :arg graph: A :class:`collections.abc.Mapping` representing a directed
+        graph. The dictionary contains one key representing each node in the
+        graph, and this key maps to a :class:`collections.abc.Collection` of nodes
+        that are connected to the node by outgoing edges.
+    """
+    if not graph:
+        # https://cs.stackexchange.com/questions/52815/is-a-graph-of-zero-nodes-vertices-connected
+        return True
+
+    visited = set()
+
+    undirected_graph = {node: set(children) for node, children in graph.items()}
+
+    for node, children in graph.items():
+        for child in children:
+            undirected_graph[child].add(node)
+
+    def dfs(node: T) -> None:
+        visited.add(node)
+        for child in undirected_graph[node]:
+            if child not in visited:
+                dfs(child)
+
+    dfs(next(iter(graph.keys())))
+
+    return visited == graph.keys()
+
+
 # vim: foldmethod=marker
diff --git a/test/test_graph_tools.py b/test/test_graph_tools.py
index 701cd5776b25959b4d26bbe8be54651f20c11104..2f14f1ada23809ef84e6c57a7cfa5bcd85170742 100644
--- a/test/test_graph_tools.py
+++ b/test/test_graph_tools.py
@@ -348,6 +348,53 @@ def test_validate_graph():
     validate_graph({})
 
 
+def test_is_connected():
+    from pytools.graph import is_connected
+    graph1 = {
+            "d": set("c"),
+            "b": set("a"),
+            "a": set(),
+            "c": set("a"),
+            }
+
+    assert is_connected(graph1)
+
+    graph2 = {
+            "d": set("d"),
+            "b": set("c"),
+            "a": set("b"),
+            "c": set("a"),
+            }
+
+    assert not is_connected(graph2)
+
+    graph3 = {
+        "a": {"b", "c"},
+        "b": {"d", "e"},
+        "c": {"d", "f"},
+        "d": set(),
+        "e": set(),
+        "f": {"g"},
+        "g": {},
+        }
+
+    assert is_connected(graph3)
+
+    graph4 = {
+        "a": {"c"},
+        "b": {"d", "e"},
+        "c": {"f"},
+        "d": set(),
+        "e": set(),
+        "f": {"g"},
+        "g": {},
+        }
+
+    assert not is_connected(graph4)
+
+    assert is_connected({})
+
+
 if __name__ == "__main__":
     if len(sys.argv) > 1:
         exec(sys.argv[1])