diff --git a/cai_causal_graph/time_series_causal_graph.py b/cai_causal_graph/time_series_causal_graph.py
index d7989b0..76d33ae 100644
--- a/cai_causal_graph/time_series_causal_graph.py
+++ b/cai_causal_graph/time_series_causal_graph.py
@@ -306,7 +306,16 @@ def get_minimal_graph(self) -> TimeSeriesCausalGraph:
                 if (
                     minimal_cg.variables is None or variable not in minimal_cg.variables
                 ) and not minimal_cg.node_exists(variable):
-                    minimal_cg.add_node(variable)
+                    # Guaranteed there is at least one node, take the first for simplicity.
+                    # This aligns with how edges are chosen for minimal graph.
+                    # Only issue is if they have different meta. TODO: CAUSALAI-4784
+                    original_floating_node = self.get_nodes_for_variable_name(variable)[0]
+                    new_floating_node = self._NodeCls(
+                        identifier=variable,
+                        meta=original_floating_node.meta,
+                        variable_type=original_floating_node.variable_type,
+                    )
+                    minimal_cg.add_node(node=new_floating_node)
 
         return minimal_cg
 
diff --git a/changelog.md b/changelog.md
index 2580732..f8339e8 100644
--- a/changelog.md
+++ b/changelog.md
@@ -1,5 +1,12 @@
 # Changelog
 
+## NEXT
+
+- Fixed a bug where metadata on floating nodes would not be correctly carried over to the minimal graph when calling
+  `cai_causal_graph.time_series_causal_graph.TimeSeriesCausalGraph.get_minimal_graph`. This also fixes an issue where
+  `cai_causal_graph.time_series_causal_graph.TimeSeriesCausalGraph.is_minimal_graph` could return `False` on minimal
+  graphs that contain floating nodes.
+
 ## 0.4.8
 
 - Upgraded `docs-builder` dependency to `"~0.2.1"` in the Makefile and updated syntax to support newer `poetry`.
diff --git a/tests/test_time_series_graph.py b/tests/test_time_series_graph.py
index a8141bd..52af9fc 100644
--- a/tests/test_time_series_graph.py
+++ b/tests/test_time_series_graph.py
@@ -1931,3 +1931,73 @@ def test_remove_non_existent_node_raises(self):
         ts_graph._remove_node_from_cache(ts_graph.get_node(ts_graph._NodeCls.identifier_from('B')))
         with self.assertRaises(ValueError):
             ts_graph.delete_node('B')
+
+    def test_floating_nodes_correctly_added_to_minimal_graph(self):
+        cg = TimeSeriesCausalGraph()
+        cg.add_time_edge('a', -1, 'a', 0)
+        cg.add_time_edge('a', 0, 'b', 0)
+        cg.add_time_edge('a', -1, 'b', -1)
+        cg.add_node(
+            variable_name='floating', time_lag=0, meta={'some': 'metadata'}, variable_type=NodeVariableType.BINARY
+        )
+
+        self.assertFalse(cg.is_minimal_graph())
+
+        minimal_graph = cg.get_minimal_graph()
+
+        self.assertTrue(minimal_graph.is_minimal_graph())
+
+        minimal_node = minimal_graph.get_node('floating')
+        self.assertEqual(minimal_node.meta['some'], 'metadata')
+        self.assertEqual(minimal_node.variable_type, NodeVariableType.BINARY)
+        self.assertEqual(minimal_node.time_lag, 0)
+
+    def test_lagged_floating_nodes_correctly_added_to_minimal_graph(self):
+        """Same as previous test, but floating node is lagged. It should still be at lag=0 in the minimal graph."""
+        cg = TimeSeriesCausalGraph()
+        cg.add_time_edge('a', -1, 'a', 0)
+        cg.add_time_edge('a', 0, 'b', 0)
+        cg.add_time_edge('a', -1, 'b', -1)
+        cg.add_node(
+            variable_name='floating', time_lag=-1, meta={'some': 'metadata'}, variable_type=NodeVariableType.BINARY
+        )
+
+        self.assertFalse(cg.is_minimal_graph())
+
+        minimal_graph = cg.get_minimal_graph()
+
+        self.assertTrue(minimal_graph.is_minimal_graph())
+
+        minimal_node = minimal_graph.get_node('floating')
+        self.assertEqual(minimal_node.meta['some'], 'metadata')
+        self.assertEqual(minimal_node.variable_type, NodeVariableType.BINARY)
+        self.assertEqual(minimal_node.time_lag, 0)
+
+        # Add td=0 floating as well to ensure we end up with 1.
+        cg.add_node(
+            variable_name='floating', time_lag=0, meta={'some more': 'metadata'}, variable_type=NodeVariableType.BINARY
+        )
+
+        # Add another floating node so minimal graph should have 2 floating nodes at td=0.
+        cg.add_node(
+            variable_name='floating_cont',
+            time_lag=-1,
+            meta={'some cont': 'metadata'},
+            variable_type=NodeVariableType.CONTINUOUS,
+        )
+
+        self.assertFalse(cg.is_minimal_graph())
+
+        minimal_graph = cg.get_minimal_graph()
+
+        self.assertTrue(minimal_graph.is_minimal_graph())
+
+        floating_node = minimal_graph.get_node('floating')
+        self.assertEqual(floating_node.meta['some'], 'metadata')  # it takes meta from td=-1 as it is first
+        self.assertEqual(floating_node.variable_type, NodeVariableType.BINARY)
+        self.assertEqual(floating_node.time_lag, 0)
+
+        floating_cont_node = minimal_graph.get_node('floating_cont')
+        self.assertEqual(floating_cont_node.meta['some cont'], 'metadata')
+        self.assertEqual(floating_cont_node.variable_type, NodeVariableType.CONTINUOUS)
+        self.assertEqual(floating_cont_node.time_lag, 0)