Update from Google.

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diff --git a/src/main/java/com/google/devtools/build/lib/graph/Digraph.java b/src/main/java/com/google/devtools/build/lib/graph/Digraph.java
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+++ b/src/main/java/com/google/devtools/build/lib/graph/Digraph.java
@@ -0,0 +1,1063 @@
+// Copyright 2014 Google Inc. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//    http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package com.google.devtools.build.lib.graph;
+
+import com.google.common.collect.ImmutableSet;
+import com.google.common.collect.Maps;
+import com.google.common.collect.Ordering;
+
+import java.util.ArrayList;
+import java.util.Collection;
+import java.util.Collections;
+import java.util.Comparator;
+import java.util.HashMap;
+import java.util.HashSet;
+import java.util.LinkedList;
+import java.util.List;
+import java.util.Map;
+import java.util.PriorityQueue;
+import java.util.Set;
+
+/**
+ * <p> {@code Digraph} a generic directed graph or "digraph", suitable for
+ * modeling asymmetric binary relations. </p>
+ *
+ * <p> An instance <code>G = &lt;V,E&gt;</code> consists of a set of nodes or
+ * vertices <code>V</code>, and a set of directed edges <code>E</code>, which
+ * is a subset of <code>V &times; V</code>.  This permits self-edges but does
+ * not represent multiple edges between the same pair of nodes. </p>
+ *
+ * <p> Nodes may be labeled with values of any type (type parameter
+ * T).  All nodes within a graph have distinct labels.  The null
+ * pointer is not a valid label.</p>
+ *
+ * <p> The package supports various operations for modeling partial order
+ * relations, and supports input/output in AT&amp;T's 'dot' format.  See
+ * http://www.research.att.com/sw/tools/graphviz/. </p>
+ *
+ * <p> Some invariants: </p>
+ * <ul>
+ *
+ * <li> Each graph instances "owns" the nodes is creates.  The behaviour of
+ * operations on nodes a graph does not own is undefined.
+ *
+ * <li> {@code Digraph} assumes immutability of node labels, much like {@link
+ * HashMap} assumes it for keys.
+ *
+ * <li> Mutating the underlying graph invalidates any sets and iterators backed
+ * by it.
+ *
+ * </ul>
+ *
+ * <p>Each node stores successor and predecessor adjacency sets using a
+ * representation that dynamically changes with size: small sets are stored as
+ * arrays, large sets using hash tables.  This representation provides
+ * significant space and time performance improvements upon two prior versions:
+ * the earliest used only HashSets; a later version used linked lists, as
+ * described in Cormen, Leiserson &amp; Rivest.
+ */
+public final class Digraph<T> implements Cloneable {
+
+  /**
+   * Maps labels to nodes, which are in strict 1:1 correspondence.
+   */
+  private final HashMap<T, Node<T>> nodes = Maps.newHashMap();
+
+  /**
+   * A source of unique, deterministic hashCodes for {@link Node} instances.
+   */
+  private int nextHashCode = 0;
+
+  /**
+   * Construct an empty Digraph.
+   */
+  public Digraph() {}
+
+  /**
+   * Sanity-check: assert that a node is indeed a member of this graph and not
+   * another one.  Perform this check whenever a function is supplied a node by
+   * the user.
+   */
+  private final void checkNode(Node<T> node) {
+    if (getNode(node.getLabel()) != node) {
+      throw new IllegalArgumentException("node " + node
+                                         + " is not a member of this graph");
+    }
+  }
+
+  /**
+   * Adds a directed edge between the nodes labelled 'from' and 'to', creating
+   * them if necessary.
+   *
+   * @return true iff the edge was not already present.
+   */
+  public boolean addEdge(T from, T to) {
+    Node<T> fromNode = createNode(from);
+    Node<T> toNode   = createNode(to);
+    return addEdge(fromNode, toNode);
+  }
+
+  /**
+   * Adds a directed edge between the specified nodes, which must exist and
+   * belong to this graph.
+   *
+   * @return true iff the edge was not already present.
+   *
+   * Note: multi-edges are ignored.  Self-edges are permitted.
+   */
+  public boolean addEdge(Node<T> fromNode, Node<T> toNode) {
+    checkNode(fromNode);
+    checkNode(toNode);
+    boolean isNewSuccessor = fromNode.addSuccessor(toNode);
+    boolean isNewPredecessor = toNode.addPredecessor(fromNode);
+    if (isNewPredecessor != isNewSuccessor) {
+      throw new IllegalStateException();
+    }
+    return isNewSuccessor;
+  }
+
+  /**
+   * Returns true iff the graph contains an edge between the
+   * specified nodes, which must exist and belong to this graph.
+   */
+  public boolean containsEdge(Node<T> fromNode, Node<T> toNode) {
+    checkNode(fromNode);
+    checkNode(toNode);
+    // TODO(bazel-team): (2009) iterate only over the shorter of from.succs, to.preds.
+    return fromNode.getSuccessors().contains(toNode);
+  }
+
+  /**
+   * Removes the edge between the specified nodes.  Idempotent: attempts to
+   * remove non-existent edges have no effect.
+   *
+   * @return true iff graph changed.
+   */
+  public boolean removeEdge(Node<T> fromNode, Node<T> toNode) {
+    checkNode(fromNode);
+    checkNode(toNode);
+    boolean changed = fromNode.removeSuccessor(toNode);
+    if (changed) {
+      toNode.removePredecessor(fromNode);
+    }
+    return changed;
+  }
+
+  /**
+   * Remove all nodes and edges.
+   */
+  public void clear() {
+    nodes.clear();
+  }
+
+  @Override
+  public String toString() {
+    return "Digraph[" + getNodeCount() + " nodes]";
+  }
+
+  @Override
+  public int hashCode() {
+    throw new UnsupportedOperationException(); // avoid nondeterminism
+  }
+
+  /**
+   * Returns true iff the two graphs are equivalent, i.e. have the same set
+   * of node labels, with the same connectivity relation.
+   *
+   * O(n^2) in the worst case, i.e. equivalence.  The algorithm could be speed up by
+   * close to a factor 2 in the worst case by a more direct implementation instead
+   * of using isSubgraph twice.
+   */
+  @Override
+  public boolean equals(Object thatObject) {
+    /* If this graph is a subgraph of thatObject, then we know that thatObject is of
+     * type Digraph<?> and thatObject can be cast to this type.
+     */
+    return isSubgraph(thatObject) && ((Digraph<?>) thatObject).isSubgraph(this);
+  }
+
+  /**
+   * Returns true iff this graph is a subgraph of the argument. This means that this graph's nodes
+   * are a subset of those of the argument; moreover, for each node of this graph the set of
+   * successors is a subset of those of the corresponding node in the argument graph.
+   *
+   * This algorithm is O(n^2), but linear in the total sizes of the graphs.
+   */
+  public boolean isSubgraph(Object thatObject) {
+    if (this == thatObject) {
+      return true;
+    }
+    if (!(thatObject instanceof Digraph)) {
+      return false;
+    }
+
+    @SuppressWarnings("unchecked")
+    Digraph<T> that = (Digraph<T>) thatObject;
+    if (this.getNodeCount() > that.getNodeCount()) {
+      return false;
+    }
+    for (Node<T> n1: nodes.values()) {
+      Node<T> n2 = that.getNodeMaybe(n1.getLabel());
+      if (n2 == null) {
+        return false; // 'that' is missing a node
+      }
+
+      // Now compare the successor relations.
+      // Careful:
+      // - We can't do simple equality on the succs-sets because the
+      //   nodes belong to two different graphs!
+      // - There's no need to check both predecessor and successor
+      //   relations, either one is sufficient.
+      Collection<Node<T>> n1succs = n1.getSuccessors();
+      Collection<Node<T>> n2succs = n2.getSuccessors();
+      if (n1succs.size() > n2succs.size()) {
+        return false;
+      }
+      // foreach successor of n1, ensure n2 has a similarly-labeled succ.
+      for (Node<T> succ1: n1succs) {
+        Node<T> succ2 = that.getNodeMaybe(succ1.getLabel());
+        if (succ2 == null) {
+          return false;
+        }
+        if (!n2succs.contains(succ2)) {
+          return false;
+        }
+      }
+    }
+    return true;
+  }
+
+  /**
+   * Returns a duplicate graph with the same set of node labels and the same
+   * connectivity relation.  The labels themselves are not cloned.
+   */
+  @Override
+  public Digraph<T> clone() {
+    final Digraph<T> that = new Digraph<T>();
+    visitNodesBeforeEdges(new AbstractGraphVisitor<T>() {
+      @Override
+      public void visitEdge(Node<T> lhs, Node<T> rhs) {
+        that.addEdge(lhs.getLabel(), rhs.getLabel());
+      }
+      @Override
+      public void visitNode(Node<T> node) {
+        that.createNode(node.getLabel());
+      }
+    });
+    return that;
+  }
+
+  /**
+   * Returns a deterministic immutable view of the nodes of this graph.
+   */
+  public Collection<Node<T>> getNodes(final Comparator<T> comparator) {
+    Ordering<Node<T>> ordering = new Ordering<Node<T>>() {
+      @Override
+      public int compare(Node<T> o1, Node<T> o2) {
+        return comparator.compare(o1.getLabel(), o2.getLabel());
+      }
+    };
+    return ordering.immutableSortedCopy(nodes.values());
+  }
+
+  /**
+   * Returns an immutable view of the nodes of this graph.
+   *
+   * Note: we have to return Collection and not Set because values() returns
+   * one: the 'nodes' HashMap doesn't know that it is injective.  :-(
+   */
+  public Collection<Node<T>> getNodes() {
+    return Collections.unmodifiableCollection(nodes.values());
+  }
+
+  /**
+   * @return the set of root nodes: those with no predecessors.
+   *
+   * NOTE: in a cyclic graph, there may be nodes that are not reachable from
+   * any "root".
+   */
+  public Set<Node<T>> getRoots() {
+    Set<Node<T>> roots = new HashSet<Node<T>>();
+    for (Node<T> node: nodes.values()) {
+      if (!node.hasPredecessors()) {
+        roots.add(node);
+      }
+    }
+    return roots;
+  }
+
+  /**
+   * @return the set of leaf nodes: those with no successors.
+   */
+  public Set<Node<T>> getLeaves() {
+    Set<Node<T>> leaves = new HashSet<Node<T>>();
+    for (Node<T> node: nodes.values()) {
+      if (!node.hasSuccessors()) {
+        leaves.add(node);
+      }
+    }
+    return leaves;
+  }
+
+  /**
+   * @return an immutable view of the set of labels of this graph's nodes.
+   */
+  public Set<T> getLabels() {
+    return Collections.unmodifiableSet(nodes.keySet());
+  }
+
+  /**
+   * Finds and returns the node with the specified label.  If there is no such
+   * node, an exception is thrown.  The null pointer is not a valid label.
+   *
+   * @return the node whose label is "label".
+   * @throws IllegalArgumentException if no node was found with the specified
+   * label.
+   */
+  public Node<T> getNode(T label) {
+    if (label == null) {
+      throw new NullPointerException();
+    }
+    Node<T> node = nodes.get(label);
+    if (node == null) {
+      throw new IllegalArgumentException("No such node label: " + label);
+    }
+    return node;
+  }
+
+  /**
+   * Find the node with the specified label.  Returns null if it doesn't exist.
+   * The null pointer is not a valid label.
+   *
+   * @return the node whose label is "label", or null if it was not found.
+   */
+  public Node<T> getNodeMaybe(T label) {
+    if (label == null) {
+      throw new NullPointerException();
+    }
+    return nodes.get(label);
+  }
+
+  /**
+   * @return the number of nodes in the graph.
+   */
+  public int getNodeCount() {
+    return nodes.size();
+  }
+
+  /**
+   * @return the number of edges in the graph.
+   *
+   * Note: expensive! Useful when asserting against mutations though.
+   */
+  public int getEdgeCount() {
+    int edges = 0;
+    for (Node<T> node: nodes.values()) {
+      edges += node.getSuccessors().size();
+    }
+    return edges;
+  }
+
+  /**
+   * Find or create a node with the specified label.  This is the <i>only</i>
+   * factory of Nodes.  The null pointer is not a valid label.
+   */
+  public Node<T> createNode(T label) {
+    if (label == null) {
+      throw new NullPointerException();
+    }
+    Node<T> n = nodes.get(label);
+    if (n == null) {
+      nodes.put(label, n = new Node<T>(label, nextHashCode++));
+    }
+    return n;
+  }
+
+  /******************************************************************
+   *                                                                *
+   *                        Graph Algorithms                        *
+   *                                                                *
+   ******************************************************************/
+
+  /**
+   * These only manipulate the graph through methods defined above.
+   */
+
+  /**
+   * Returns true iff the graph is cyclic.  Time: O(n).
+   */
+  public boolean isCyclic() {
+
+    // To detect cycles, we use a colored depth-first search. All nodes are
+    // initially marked white.  When a node is encountered, it is marked grey,
+    // and when its descendants are completely visited, it is marked black.
+    // If a grey node is ever encountered, then there is a cycle.
+    final Object WHITE = null; // i.e. not present in nodeToColor, the default.
+    final Object GREY  = new Object();
+    final Object BLACK = new Object();
+    final Map<Node<T>, Object> nodeToColor =
+      new HashMap<Node<T>, Object>(); // empty => all white
+
+    class CycleDetector { /* defining a class gives us lexical scope */
+      boolean visit(Node<T> node) {
+        nodeToColor.put(node, GREY);
+        for (Node<T> succ: node.getSuccessors()) {
+          if (nodeToColor.get(succ) == GREY) {
+            return true;
+          } else if (nodeToColor.get(succ) == WHITE) {
+            if (visit(succ)) {
+              return true;
+            }
+          }
+        }
+        nodeToColor.put(node, BLACK);
+        return false;
+      }
+    }
+
+    CycleDetector detector = new CycleDetector();
+    for (Node<T> node: nodes.values()) {
+      if (nodeToColor.get(node) == WHITE) {
+        if (detector.visit(node)) {
+          return true;
+        }
+      }
+    }
+    return false;
+  }
+
+  /**
+   * Returns the strong component graph of "this".  That is, returns a new
+   * acyclic graph in which all strongly-connected components in the original
+   * graph have been "fused" into a single node.
+   *
+   * @return a new graph, whose node labels are sets of nodes of the
+   * original graph.  (Do not get confused as to which graph each
+   * set of Nodes belongs!)
+   */
+  public Digraph<Set<Node<T>>> getStrongComponentGraph() {
+    Collection<Set<Node<T>>> sccs = getStronglyConnectedComponents();
+    Digraph<Set<Node<T>>> scGraph = createImageUnderPartition(sccs);
+    scGraph.removeSelfEdges(); // scGraph should be acyclic: no self-edges
+    return scGraph;
+  }
+
+  /**
+   * Returns a partition of the nodes of this graph into sets, each set being
+   * one strongly-connected component of the graph.
+   */
+  public Collection<Set<Node<T>>> getStronglyConnectedComponents() {
+    final List<Set<Node<T>>> sccs = new ArrayList<Set<Node<T>>>();
+    NodeSetReceiver<T> r = new NodeSetReceiver<T>() {
+      @Override
+      public void accept(Set<Node<T>> scc) {
+        sccs.add(scc);
+      }
+    };
+    SccVisitor<T> v = new SccVisitor<T>();
+    for (Node<T> node : nodes.values()) {
+      v.visit(r, node);
+    }
+    return sccs;
+  }
+
+  /**
+   * <p> Given a partition of the graph into sets of nodes, returns the image
+   * of this graph under the function which maps each node to the
+   * partition-set in which it appears.  The labels of the new graph are the
+   * (immutable) sets of the partition, and the edges of the new graph are the
+   * edges of the original graph, mapped via the same function. </p>
+   *
+   * <p> Note: the resulting graph may contain self-edges.  If these are not
+   * wanted, call <code>removeSelfEdges()</code>> on the result. </p>
+   *
+   * <p> Interesting special case: if the partition is the set of
+   * strongly-connected components, the result of this function is the
+   * strong-component graph. </p>
+   */
+  public Digraph<Set<Node<T>>>
+    createImageUnderPartition(Collection<Set<Node<T>>> partition) {
+
+    // Build mapping function: each node label is mapped to its equiv class:
+    Map<T, Set<Node<T>>> labelToImage =
+      new HashMap<T, Set<Node<T>>>();
+    for (Set<Node<T>> set: partition) {
+      // It's important to use immutable sets of node labels when sets are keys
+      // in a map; see ImmutableSet class for explanation.
+      Set<Node<T>> imageSet = ImmutableSet.copyOf(set);
+      for (Node<T> node: imageSet) {
+        labelToImage.put(node.getLabel(), imageSet);
+      }
+    }
+
+    if (labelToImage.size() != getNodeCount()) {
+      throw new IllegalArgumentException(
+          "createImageUnderPartition(): argument is not a partition");
+    }
+
+    return createImageUnderMapping(labelToImage);
+  }
+
+  /**
+   * Returns the image of this graph in a given function, expressed as a
+   * mapping from labels to some other domain.
+   */
+  public <IMAGE> Digraph<IMAGE>
+    createImageUnderMapping(Map<T, IMAGE> map) {
+
+    Digraph<IMAGE> imageGraph = new Digraph<IMAGE>();
+
+    for (Node<T> fromNode: nodes.values()) {
+      T fromLabel = fromNode.getLabel();
+
+      IMAGE fromImage = map.get(fromLabel);
+      if (fromImage == null) {
+        throw new IllegalArgumentException(
+            "Incomplete function: undefined for " + fromLabel);
+      }
+      imageGraph.createNode(fromImage);
+
+      for (Node<T> toNode: fromNode.getSuccessors()) {
+        T toLabel = toNode.getLabel();
+
+        IMAGE toImage = map.get(toLabel);
+        if (toImage == null) {
+          throw new IllegalArgumentException(
+            "Incomplete function: undefined for " + toLabel);
+        }
+        imageGraph.addEdge(fromImage, toImage);
+      }
+    }
+
+    return imageGraph;
+  }
+
+  /**
+   * Removes any self-edges (x,x) in this graph.
+   */
+  public void removeSelfEdges() {
+    for (Node<T> node: nodes.values()) {
+      removeEdge(node, node);
+    }
+  }
+
+  /**
+   * Finds the shortest directed path from "fromNode" to "toNode".  The path is
+   * returned as an ordered list of nodes, including both endpoints.  Returns
+   * null if there is no path.  Uses breadth-first search.  Running time is
+   * O(n).
+   */
+  public List<Node<T>> getShortestPath(Node<T> fromNode,
+                                           Node<T> toNode) {
+    checkNode(fromNode);
+    checkNode(toNode);
+
+    if (fromNode == toNode) {
+      return Collections.singletonList(fromNode);
+    }
+
+    Map<Node<T>, Node<T>> pathPredecessor =
+      new HashMap<Node<T>, Node<T>>();
+
+    Set<Node<T>> marked = new HashSet<Node<T>>();
+
+    LinkedList<Node<T>> queue = new LinkedList<Node<T>>();
+    queue.addLast(fromNode);
+    marked.add(fromNode);
+
+    while (queue.size() > 0) {
+      Node<T> u = queue.removeFirst();
+      for (Node<T> v: u.getSuccessors()) {
+        if (marked.add(v)) {
+          pathPredecessor.put(v, u);
+          if (v == toNode) {
+            return getPathToTreeNode(pathPredecessor, v); // found a path
+          }
+          queue.addLast(v);
+        }
+      }
+    }
+    return null; // no path
+  }
+
+  /**
+   * Given a tree (expressed as a map from each node to its parent), and a
+   * starting node, returns the path from the root of the tree to 'node' as a
+   * list.
+   */
+  private static <X> List<X> getPathToTreeNode(Map<X, X> tree, X node) {
+    List<X> path = new ArrayList<X>();
+    while (node != null) {
+      path.add(node);
+      node = tree.get(node); // get parent
+    }
+    Collections.reverse(path);
+    return path;
+  }
+
+  /**
+   * Returns the nodes of an acyclic graph in topological order
+   * [a.k.a "reverse post-order" of depth-first search.]
+   *
+   * A topological order is one such that, if (u, v) is a path in
+   * acyclic graph G, then u is before v in the topological order.
+   * In other words "tails before heads" or "roots before leaves".
+   *
+   * @return The nodes of the graph, in a topological order
+   */
+  public List<Node<T>> getTopologicalOrder() {
+    List<Node<T>> order = getPostorder();
+    Collections.reverse(order);
+    return order;
+  }
+
+  /**
+   * Returns the nodes of an acyclic graph in topological order
+   * [a.k.a "reverse post-order" of depth-first search.]
+   *
+   * A topological order is one such that, if (u, v) is a path in
+   * acyclic graph G, then u is before v in the topological order.
+   * In other words "tails before heads" or "roots before leaves".
+   *
+   * If an ordering is given, returns a specific topological order from the set
+   * of all topological orders; if no ordering given, returns an arbitrary
+   * (nondeterministic) one, but is a bit faster because no sorting needs to be
+   * done for each node.
+   *
+   * @param edgeOrder the ordering in which edges originating from the same node
+   *     are visited.
+   * @return The nodes of the graph, in a topological order
+   */
+  public List<Node<T>> getTopologicalOrder(
+      Comparator<T> edgeOrder) {
+    CollectingVisitor<T> visitor = new CollectingVisitor<T>();
+    DFS<T> visitation = new DFS<T>(DFS.Order.POSTORDER, edgeOrder, false);
+    visitor.beginVisit();
+    for (Node<T> node : getNodes(edgeOrder)) {
+      visitation.visit(node, visitor);
+    }
+    visitor.endVisit();
+
+    List<Node<T>> order = visitor.getVisitedNodes();
+    Collections.reverse(order);
+    return order;
+  }
+
+  /**
+   * Returns the nodes of an acyclic graph in post-order.
+   */
+  public List<Node<T>> getPostorder() {
+    CollectingVisitor<T> collectingVisitor = new CollectingVisitor<T>();
+    visitPostorder(collectingVisitor);
+    return collectingVisitor.getVisitedNodes();
+  }
+
+  /**
+   * Returns the (immutable) set of nodes reachable from node 'n' (reflexive
+   * transitive closure).
+   */
+  public Set<Node<T>> getFwdReachable(Node<T> n) {
+    return getFwdReachable(Collections.singleton(n));
+  }
+
+  /**
+   * Returns the (immutable) set of nodes reachable from any node in {@code
+   * startNodes} (reflexive transitive closure).
+   */
+  public Set<Node<T>> getFwdReachable(Collection<Node<T>> startNodes) {
+    // This method is intentionally not static, to permit future expansion.
+    DFS<T> dfs = new DFS<T>(DFS.Order.PREORDER, false);
+    for (Node<T> n : startNodes) {
+      dfs.visit(n, new AbstractGraphVisitor<T>());
+    }
+    return dfs.getMarked();
+  }
+
+  /**
+   * Returns the (immutable) set of nodes that reach node 'n' (reflexive
+   * transitive closure).
+   */
+  public Set<Node<T>> getBackReachable(Node<T> n) {
+    return getBackReachable(Collections.singleton(n));
+  }
+
+  /**
+   * Returns the (immutable) set of nodes that reach some node in {@code
+   * startNodes} (reflexive transitive closure).
+   */
+  public Set<Node<T>> getBackReachable(Collection<Node<T>> startNodes) {
+    // This method is intentionally not static, to permit future expansion.
+    DFS<T> dfs = new DFS<T>(DFS.Order.PREORDER, true);
+    for (Node<T> n : startNodes) {
+      dfs.visit(n, new AbstractGraphVisitor<T>());
+    }
+    return dfs.getMarked();
+  }
+
+  /**
+   * Removes the node in the graph specified by the given label.  Optionally,
+   * preserves the graph order (by connecting up the broken edges) or drop them
+   * all.  If the specified label is not the label of any node in the graph,
+   * does nothing.
+   *
+   * @param label the label of the node to remove.
+   * @param preserveOrder if true, adds edges between the neighbours
+   *   of the removed node so as to maintain the graph ordering
+   *   relation between all pairs of such nodes.  If false, simply
+   *   discards all edges from the deleted node to its neighbours.
+   * @return true iff 'label' identifies a node (i.e. the graph was changed).
+   */
+  public boolean removeNode(T label, boolean preserveOrder) {
+    Node<T> node = getNodeMaybe(label);
+    if (node != null) {
+      removeNode(node, preserveOrder);
+      return true;
+    } else {
+      return false;
+    }
+  }
+
+  /**
+   * Removes the specified node in the graph.
+   *
+   * @param n the node to remove (must be in the graph).
+   * @param preserveOrder see removeNode(T, boolean).
+   */
+  public void removeNode(Node<T> n, boolean preserveOrder) {
+    checkNode(n);
+    for (Node<T> b:  n.getSuccessors()) { // edges from n
+      // exists: n -> b
+      if (preserveOrder) {
+        for (Node<T> a: n.getPredecessors()) { // edges to n
+          // exists: a -> n
+          // beware self edges: they prevent n's deletion!
+          if (a != n && b != n) {
+            addEdge(a, b); // concurrent mod?
+          }
+        }
+      }
+      b.removePredecessor(n); // remove edge n->b in b
+    }
+    for (Node<T> a: n.getPredecessors()) { // edges to n
+      a.removeSuccessor(n); // remove edge a->n in a
+    }
+
+    n.removeAllEdges(); // remove edges b->n and a->n in n
+    Object del = nodes.remove(n.getLabel());
+    if (del != n) {
+      throw new IllegalStateException(del + " " + n);
+    }
+  }
+
+  /**
+   * Extracts the subgraph G' of this graph G, containing exactly the nodes
+   * specified by the labels in V', and preserving the original
+   * <i>transitive</i> graph relation among those nodes. </p>
+   *
+   * @param subset a subset of the labels of this graph; the resulting graph
+   * will have only the nodes with these labels.
+   */
+  public Digraph<T> extractSubgraph(final Set<T> subset) {
+    Digraph<T> subgraph = this.clone();
+    subgraph.subgraph(subset);
+    return subgraph;
+  }
+
+  /**
+   * Removes all nodes from this graph except those whose label is an element of {@code keepLabels}.
+   * Edges are added so as to preserve the <i>transitive</i> closure relation.
+   *
+   * @param keepLabels a subset of the labels of this graph; the resulting graph
+   * will have only the nodes with these labels.
+   */
+  public void subgraph(final Set<T> keepLabels) {
+    // This algorithm does the following:
+    // Let keep = nodes that have labels in keepLabels.
+    // Let toRemove = nodes \ keep. reachables = successors and predecessors of keep in nodes.
+    // reachables is the subset of nodes of remove that are an immediate neighbor of some node in
+    // keep.
+    //
+    // Removes all nodes of reachables from keepLabels.
+    // Until reachables is empty:
+    //   Takes n from reachables
+    //   for all s in succ(n)
+    //     for all p in pred(n)
+    //       add the edge (p, s)
+    //     add s to reachables
+    //   for all p in pred(n)
+    //     add p to reachables
+    //   Remove n and its edges
+    //
+    // A few adjustments are needed to do the whole computation.
+
+    final Set<Node<T>> toRemove = new HashSet<>();
+    final Set<Node<T>> keepNeighbors = new HashSet<>();
+
+    // Look for all nodes if they are to be kept or removed
+    for (Node<T> node : nodes.values()) {
+      if (keepLabels.contains(node.getLabel())) {
+        // Node is to be kept
+        keepNeighbors.addAll(node.getPredecessors());
+        keepNeighbors.addAll(node.getSuccessors());
+      } else {
+        // node is to be removed.
+        toRemove.add(node);
+      }
+    }
+
+    if (toRemove.isEmpty()) {
+      // This premature return is needed to avoid 0-size priority queue creation.
+      return;
+    }
+
+    // We use a priority queue to look for low-order nodes first so we don't propagate the high
+    // number of paths of high-order nodes making the time consumption explode.
+    // For perfect results we should reorder the set each time we add a new edge but this would
+    // be too expensive, so this is a good enough approximation.
+    final PriorityQueue<Node<T>> reachables = new PriorityQueue<>(toRemove.size(),
+        new Comparator<Node<T>>() {
+      @Override
+      public int compare(Node<T> o1, Node<T> o2) {
+        return Long.compare((long) o1.numPredecessors() * (long) o1.numSuccessors(),
+            (long) o2.numPredecessors() * (long) o2.numSuccessors());
+      }
+    });
+
+    // Construct the reachables queue with the list of successors and predecessors of keep in
+    // toRemove.
+    keepNeighbors.retainAll(toRemove);
+    reachables.addAll(keepNeighbors);
+    toRemove.removeAll(reachables);
+
+    // Remove nodes, least connected first, preserving reachability.
+    while (!reachables.isEmpty()) {
+      Node<T> node = reachables.poll();
+      for (Node<T> s : node.getSuccessors()) {
+        if (s == node) { continue; } // ignore self-edge
+
+        for (Node<T> p : node.getPredecessors()) {
+          if (p == node) { continue; } // ignore self-edge
+          addEdge(p, s);
+        }
+
+        // removes n -> s
+        s.removePredecessor(node);
+        if (toRemove.remove(s)) {
+          reachables.add(s);
+        }
+      }
+
+      for (Node<T> p : node.getPredecessors()) {
+        if (p == node) { continue; } // ignore self-edge
+        p.removeSuccessor(node);
+        if (toRemove.remove(p)) {
+          reachables.add(p);
+        }
+      }
+
+      // After the node deletion, the graph is again well-formed and the original topological order
+      // is preserved.
+      nodes.remove(node.getLabel());
+    }
+
+    // Final cleanup for non-reachable nodes.
+    for (Node<T> node : toRemove) {
+      removeNode(node, false);
+    }
+  }
+
+  private interface NodeSetReceiver<T> {
+    void accept(Set<Node<T>> nodes);
+  }
+
+  /**
+   * Find strongly connected components using path-based strong component
+   * algorithm. This has the advantage over the default method of returning
+   * the components in postorder.
+   *
+   * We visit nodes depth-first, keeping track of the order that
+   * we visit them in (preorder). Our goal is to find the smallest node (in
+   * this preorder of visitation) reachable from a given node. We keep track of the
+   * smallest node pointed to so far at the top of a stack. If we ever find an
+   * already-visited node, then if it is not already part of a component, we
+   * pop nodes from that stack until we reach this already-visited node's number
+   * or an even smaller one.
+   *
+   * Once the depth-first visitation of a node is complete, if this node's
+   * number is at the top of the stack, then it is the "first" element visited
+   * in its strongly connected component. Hence we pop all elements that were
+   * pushed onto the visitation stack and put them in a strongly connected
+   * component with this one, then send a passed-in {@link Digraph.NodeSetReceiver} this component.
+   */
+  private class SccVisitor<T> {
+    // Nodes already assigned to a strongly connected component.
+    private final Set<Node<T>> assigned = new HashSet<Node<T>>();
+    // The order each node was visited in.
+    private final Map<Node<T>, Integer> preorder = new HashMap<Node<T>, Integer>();
+    // Stack of all nodes visited whose SCC has not yet been determined. When an SCC is found,
+    // that SCC is an initial segment of this stack, and is popped off. Every time a new node is
+    // visited, it is put on this stack.
+    private final List<Node<T>> stack = new ArrayList<Node<T>>();
+    // Stack of visited indices for the first-visited nodes in each of their known-so-far
+    // strongly connected components. A node pushes its index on when it is visited. If any of
+    // its successors have already been visited and are not in an already-found strongly connected
+    // component, then, since the successor was already visited, it and this node must be part of a
+    // cycle. So every node visited since the successor is actually in the same strongly connected
+    // component. In this case, preorderStack is popped until the top is at most the successor's
+    // index.
+    //
+    // After all descendants of a node have been visited, if the top element of preorderStack is
+    // still the current node's index, then it was the first element visited of the current strongly
+    // connected component. So all nodes on {@code stack} down to the current node are in its
+    // strongly connected component. And the node's index is popped from preorderStack.
+    private final List<Integer> preorderStack = new ArrayList<Integer>();
+    // Index of node being visited.
+    private int counter = 0;
+
+    private void visit(NodeSetReceiver<T> visitor, Node<T> node) {
+      if (preorder.containsKey(node)) {
+        // This can only happen if this was a non-recursive call, and a previous
+        // visit call had already visited node.
+        return;
+      }
+      preorder.put(node, counter);
+      stack.add(node);
+      preorderStack.add(counter++);
+      int preorderLength = preorderStack.size();
+      for (Node<T> succ : node.getSuccessors()) {
+        Integer succPreorder = preorder.get(succ);
+        if (succPreorder == null) {
+          visit(visitor, succ);
+        } else {
+          // Does succ not already belong to an SCC? If it doesn't, then it
+          // must be in the same SCC as node. The "starting node" of this SCC
+          // must have been visited before succ (or is succ itself).
+          if (!assigned.contains(succ)) {
+            while (preorderStack.get(preorderStack.size() - 1) > succPreorder) {
+              preorderStack.remove(preorderStack.size() - 1);
+            }
+          }
+        }
+      }
+      if (preorderLength == preorderStack.size()) {
+        // If the length of the preorderStack is unchanged, we did not find any earlier-visited
+        // nodes that were part of a cycle with this node. So this node is the first-visited
+        // element in its strongly connected component, and we collect the component.
+        preorderStack.remove(preorderStack.size() - 1);
+        Set<Node<T>> scc = new HashSet<Node<T>>();
+        Node<T> compNode;
+        do {
+          compNode = stack.remove(stack.size() - 1);
+          assigned.add(compNode);
+          scc.add(compNode);
+        } while (!node.equals(compNode));
+        visitor.accept(scc);
+      }
+    }
+  }
+
+  /********************************************************************
+   *                                                                  *
+   *                    Orders, traversals and visitors               *
+   *                                                                  *
+   ********************************************************************/
+
+  /**
+   * A visitation over all the nodes in the graph that invokes
+   * <code>visitor.visitNode()</code> for each node in a depth-first
+   * post-order: each node is visited <i>after</i> each of its successors; the
+   * order in which edges are traversed is the order in which they were added
+   * to the graph.  <code>visitor.visitEdge()</code> is not called.
+   *
+   * @param startNodes the set of nodes from which to begin the visitation.
+   */
+  public void visitPostorder(GraphVisitor<T> visitor,
+                             Iterable<Node<T>> startNodes) {
+    visitDepthFirst(visitor, DFS.Order.POSTORDER, false, startNodes);
+  }
+
+  /**
+   * Equivalent to {@code visitPostorder(visitor, getNodes())}.
+   */
+  public void visitPostorder(GraphVisitor<T> visitor) {
+    visitPostorder(visitor, nodes.values());
+  }
+
+  /**
+   * A visitation over all the nodes in the graph that invokes
+   * <code>visitor.visitNode()</code> for each node in a depth-first
+   * pre-order: each node is visited <i>before</i> each of its successors; the
+   * order in which edges are traversed is the order in which they were added
+   * to the graph.  <code>visitor.visitEdge()</code> is not called.
+   *
+   * @param startNodes the set of nodes from which to begin the visitation.
+   */
+  public void visitPreorder(GraphVisitor<T> visitor,
+                            Iterable<Node<T>> startNodes) {
+    visitDepthFirst(visitor, DFS.Order.PREORDER, false, startNodes);
+  }
+
+  /**
+   * Equivalent to {@code visitPreorder(visitor, getNodes())}.
+   */
+  public void visitPreorder(GraphVisitor<T> visitor) {
+    visitPreorder(visitor, nodes.values());
+  }
+
+  /**
+   * A visitation over all the nodes in the graph in depth-first order.  See
+   * DFS constructor for meaning of 'order' and 'transpose' parameters.
+   *
+   * @param startNodes the set of nodes from which to begin the visitation.
+   */
+  public void visitDepthFirst(GraphVisitor<T> visitor,
+                              DFS.Order order,
+                              boolean transpose,
+                              Iterable<Node<T>> startNodes) {
+    DFS<T> visitation = new DFS<T>(order, transpose);
+    visitor.beginVisit();
+    for (Node<T> node: startNodes) {
+      visitation.visit(node, visitor);
+    }
+    visitor.endVisit();
+  }
+
+  /**
+   * A visitation over the graph that visits all nodes and edges in some order
+   * such that each node is visited before any edge coming out of that node;
+   * the order is otherwise unspecified.
+   *
+   * @param startNodes the set of nodes from which to begin the visitation.
+   */
+  public void visitNodesBeforeEdges(GraphVisitor<T> visitor,
+                                    Iterable<Node<T>> startNodes) {
+    visitor.beginVisit();
+    for (Node<T> fromNode: startNodes) {
+      visitor.visitNode(fromNode);
+      for (Node<T> toNode: fromNode.getSuccessors()) {
+        visitor.visitEdge(fromNode, toNode);
+      }
+    }
+    visitor.endVisit();
+  }
+
+  /**
+   * Equivalent to {@code visitNodesBeforeEdges(visitor, getNodes())}.
+   */
+  public void visitNodesBeforeEdges(GraphVisitor<T> visitor) {
+    visitNodesBeforeEdges(visitor, nodes.values());
+  }
+
+}