--- a/src/engines/graph/algorithms/layered/kernel/graph.rs
+++ b/src/engines/graph/algorithms/layered/kernel/graph.rs
@@ -358,6 +358,14 @@
                 compound_nodes.insert(parent_idx);
             }
         }
+        // A titled subgraph with no member nodes is nobody's parent, so the
+        // parent map above never registers it as a compound. It still lays out
+        // as an (empty) subgraph box: border construction, title insertion, and
+        // rank-span extraction all read it like a subgraph. Mermaid draws the
+        // titled cluster, so keep it here; compound_titles must stay a subset.
+        for &titled_idx in &compound_titles {
+            compound_nodes.insert(titled_idx);
+        }
 
         let model_order: Vec<Option<usize>> = (0..n).map(Some).collect();
         let mut compound_semantic_order = vec![None; n];

--- a/src/engines/graph/algorithms/layered/kernel/regression_tests.rs
+++ b/src/engines/graph/algorithms/layered/kernel/regression_tests.rs
@@ -1180,6 +1180,42 @@
 }
 
 #[test]
+fn test_layout_titled_empty_subgraph_end_to_end() {
+    // Mermaid renders `subgraph e ["label"] end` as an empty cluster box. The
+    // graph model keeps it as a titled node with no children; it is nobody's
+    // parent, so the parent map alone never registers it as a compound, and
+    // title insertion could not index a border_top for it (regression: the
+    // HashMap index panicked with "no entry found for key").
+    let mut graph: DiGraph<(f64, f64)> = DiGraph::new();
+    graph.add_node("sg1", (0.0, 0.0));
+    graph.add_node("empty_sg", (0.0, 0.0));
+    graph.add_node("A", (40.0, 20.0));
+    graph.add_node("B", (40.0, 20.0));
+    graph.add_edge("A", "B");
+    graph.set_parent("A", "sg1");
+    graph.set_parent("B", "sg1");
+    graph.set_has_title("sg1");
+    graph.set_has_title("empty_sg");
+
+    let lg = LayoutGraph::from_digraph(&graph, |_, dims| *dims);
+    for &titled in &lg.compound_titles {
+        assert!(
+            lg.compound_nodes.contains(&titled),
+            "compound_titles must stay a subset of compound_nodes"
+        );
+    }
+
+    let config = LayoutConfig::default();
+    let result = layout(&graph, &config, |_, dims| *dims);
+
+    assert!(result.nodes.contains_key(&"A".into()));
+    assert!(result.nodes.contains_key(&"B".into()));
+    assert!(result.subgraph_bounds.contains_key("sg1"));
+    // The empty compound has no member ranks; it contributes no bounds.
+    assert!(!result.subgraph_bounds.contains_key("empty_sg"));
+}
+
+#[test]
 fn test_layout_multi_level_compound_nesting() {
     let mut g: DiGraph<(f64, f64)> = DiGraph::new();
     g.add_node("A", (40.0, 20.0));