diff --git a/crates/graph/src/lib.rs b/crates/graph/src/lib.rs
index 8fa324a..d33f238 100644
--- a/crates/graph/src/lib.rs
+++ b/crates/graph/src/lib.rs
@@ -1,3 +1,5 @@
+mod util;
+
 use petgraph::{graph::NodeIndex, stable_graph::StableDiGraph, visit::EdgeRef};
 use std::cell::{Cell, RefCell};
 use std::rc::Rc;
@@ -61,9 +63,10 @@ impl<Output: Clone + 'static> Graph<Output> {
     }
 
     pub fn freeze(self) -> Result<FrozenGraph<Output>, GraphFreezeError> {
-        if self.output.is_none() {
-            return Err(GraphFreezeError::NoOutput);
-        }
+        let output: NodeIndex<u32> = match self.output {
+            None => return Err(GraphFreezeError::NoOutput),
+            Some(idx) => idx,
+        };
 
         let graph = self.node_graph.borrow();
         let indices = graph.node_indices().collect::<Vec<_>>();
@@ -80,7 +83,9 @@ impl<Output: Clone + 'static> Graph<Output> {
             self.node_graph.borrow_mut().add_edge(source, dest, ());
         }
 
-        // TODO: remove nodes not connected to output
+        let mut graph = self.node_graph.borrow_mut();
+        util::remove_nodes_not_connected_to(&mut *graph, output);
+        drop(graph);
 
         let sorted = petgraph::algo::toposort(&*self.node_graph.borrow(), None);
         if let Err(_cycle) = sorted {
@@ -147,6 +152,10 @@ impl<Output: Clone + 'static> FrozenGraph<Output> {
         node.value()
     }
 
+    pub fn node_count(&self) -> usize {
+        self.node_graph.borrow().node_count()
+    }
+
     pub fn modify<F>(&mut self, mut f: F) -> Result<(), GraphFreezeError>
     where
         F: FnMut(&mut Graph<Output>) -> (),
@@ -172,6 +181,7 @@ impl<Output: Clone + 'static> FrozenGraph<Output> {
     }
 }
 
+#[derive(Clone)]
 pub struct Input<T> {
     node_idx: NodeIndex<u32>,
     value: Rc<RefCell<Option<T>>>,
@@ -498,8 +508,8 @@ mod tests {
         let a = graph.add_rule(DeferredInput(Rc::clone(&a_input)));
         let b_input = Rc::new(RefCell::new(Some(a)));
         let b = graph.add_rule(DeferredInput(b_input));
-        *a_input.borrow_mut() = Some(b);
-        graph.set_output(Inc(0));
+        *a_input.borrow_mut() = Some(b.clone());
+        graph.set_output(Double(b));
         match graph.freeze() {
             Err(GraphFreezeError::Cyclic(_)) => (),
             Err(e) => assert!(false, "unexpected error {:?}", e),
@@ -519,5 +529,6 @@ mod tests {
             })
             .expect("modify");
         assert_eq!(frozen.evaluate(), 2);
+        assert_eq!(frozen.node_count(), 1);
     }
 }
diff --git a/crates/graph/src/util.rs b/crates/graph/src/util.rs
new file mode 100644
index 0000000..94ed6fc
--- /dev/null
+++ b/crates/graph/src/util.rs
@@ -0,0 +1,47 @@
+use petgraph::{
+    stable_graph::{IndexType, NodeIndex, StableGraph},
+    unionfind::UnionFind,
+    visit::{EdgeRef, IntoEdgeReferences, NodeIndexable},
+    EdgeType,
+};
+
+pub fn remove_nodes_not_connected_to<N, E, Ty: EdgeType, Ix: IndexType>(
+    g: &mut StableGraph<N, E, Ty, Ix>,
+    node: NodeIndex<Ix>,
+) {
+    // based on petgraph's connected_components
+    let mut vertex_sets = UnionFind::new(g.node_bound());
+    for edge in g.edge_references() {
+        vertex_sets.union(g.to_index(edge.source()), g.to_index(edge.target()));
+    }
+    let to_remove = g
+        .node_indices()
+        .filter(|other_idx| !vertex_sets.equiv(g.to_index(node), g.to_index(*other_idx)))
+        .collect::<Vec<_>>();
+    for idx in to_remove {
+        g.remove_node(idx);
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use petgraph::stable_graph::StableGraph;
+
+    #[test]
+    fn remove_nodes_not_connected_to() {
+        let mut graph: StableGraph<(), ()> = Default::default();
+        let a = graph.add_node(());
+        let b = graph.add_node(());
+        let c = graph.add_node(());
+        let d = graph.add_node(());
+        let e = graph.add_node(());
+        graph.extend_with_edges(&[(a, b), (a, c), (d, e)]);
+        super::remove_nodes_not_connected_to(&mut graph, a);
+        assert_eq!(graph.node_count(), 3);
+        assert!(graph.contains_node(a));
+        assert!(graph.contains_node(b));
+        assert!(graph.contains_node(c));
+        assert!(!graph.contains_node(d));
+        assert!(!graph.contains_node(e));
+    }
+}