diff --git a/app.py b/app.py
index 7dcfc9f..4d08384 100644
--- a/app.py
+++ b/app.py
@@ -219,6 +219,11 @@ def solve_diagram(data: DiagramData):
             return {"status": "error", "message": f"Input node '{data.input_node}' not found."}
         if data.output_node not in real_nodes:
             return {"status": "error", "message": f"Output node '{data.output_node}' not found."}
+        if not nx.has_path(G, data.input_node, data.output_node):
+            return {
+                "status": "error",
+                "message": f"No forward path from '{data.input_node}' to '{data.output_node}'.",
+            }
 
         raw_loops = list(nx.simple_cycles(G))
         loops_data = []
diff --git a/tests/test_solver.py b/tests/test_solver.py
index 26ef199..fa9725f 100644
--- a/tests/test_solver.py
+++ b/tests/test_solver.py
@@ -95,6 +95,26 @@ def test_validate_rejects_missing_output_node(self):
         self.assertEqual(result["status"], "error")
         self.assertIn("missing_output_node", {e["type"] for e in result["errors"]})
 
+    def test_solve_rejects_disconnected_output(self):
+        data = diagram(
+            [("S", "A", "G")],
+            nodes=["S", "A", "T"],
+        )
+        validated = validate_diagram(data)
+        solved = solve_diagram(data)
+        self.assertEqual(validated["status"], "error")
+        self.assertIn("no_path", {error["type"] for error in validated["errors"]})
+        self.assertEqual(solved["status"], "error")
+        self.assertIn("No forward path", solved["message"])
+        self.assertNotIn("transfer_function_expr", solved)
+
+    def test_solve_rejects_reverse_only_connection(self):
+        data = diagram([("T", "S", "H")])
+        self.assertEqual(validate_diagram(data)["status"], "error")
+        solved = solve_diagram(data)
+        self.assertEqual(solved["status"], "error")
+        self.assertIn("No forward path", solved["message"])
+
     def test_validate_reports_off_path_and_isolated_nodes(self):
         result = validate_diagram(
             diagram([("S", "T", "G")], nodes=["S", "T", "Z"])