public static <N> Traverser<N> forTree(SuccessorsFunction<N> tree) {
    if (tree instanceof BaseGraph) {
      checkArgument(((BaseGraph<?>) tree).isDirected(), "Undirected graphs can never be trees.");
    }
    if (tree instanceof Network) {
      checkArgument(((Network<?, ?>) tree).isDirected(), "Undirected networks can never be trees.");
    }
    return new Traverser<N>(tree) {
      @Override
      Traversal<N> newTraversal() {

    assertStronglyEquivalent(graph, Graphs.copyOf(graph));
    assertStronglyEquivalent(graph, ImmutableGraph.copyOf(graph));

    String graphString = graph.toString();
    assertThat(graphString).contains("isDirected: " + graph.isDirected());
    assertThat(graphString).contains("allowsSelfLoops: " + graph.allowsSelfLoops());

    int nodeStart = graphString.indexOf("nodes:");
    int edgeStart = graphString.indexOf("edges:");

   *
   * <ul>
   *   <li>A and B have equal {@link #isDirected() directedness}.
   *   <li>A and B have equal {@link #nodes() node sets}.
   *   <li>A and B have equal {@link #edges() edge sets}.
   *   <li>Every edge in A and B connects the same nodes in the same direction (if any).
   * </ul>
   *
   * <p>Network properties besides {@link #isDirected() directedness} do <b>not</b> affect equality.

    if (!(obj instanceof EndpointPair)) {
      return false;
    }
    EndpointPair<?> endpointPair = (EndpointPair<?>) obj;

    if (graph.isDirected() != endpointPair.isOrdered()) {
      return false;
    }

    if (graph.isDirected()) {
      Object source = endpointPair.source();
      Object target = endpointPair.target();
      return (node.equals(source) && successorsOrEmpty(node).contains(target))

        ValueGraphBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .<String, Integer>immutable()
            .build();

    assertThat(emptyGraph.isDirected()).isTrue();
    assertThat(emptyGraph.allowsSelfLoops()).isTrue();
    assertThat(emptyGraph.nodeOrder()).isEqualTo(ElementOrder.<String>natural());
  }

  /**

   */
  public static <N> boolean hasCycle(Graph<N> graph) {
    int numEdges = graph.edges().size();
    if (numEdges == 0) {
      return false; // An edge-free graph is acyclic by definition.
    }
    if (!graph.isDirected() && numEdges >= graph.nodes().size()) {
      return true; // Optimization for the undirected case: at least one cycle must exist.
    }

    Map<Object, NodeVisitState> visitedNodes =

        GraphBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .immutable()
            .build();

    assertThat(emptyGraph.isDirected()).isTrue();
    assertThat(emptyGraph.allowsSelfLoops()).isTrue();
    assertThat(emptyGraph.nodeOrder()).isEqualTo(ElementOrder.<String>natural());
  }

  /**

        NetworkBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .<String, Integer>immutable()
            .build();

    assertThat(emptyNetwork.isDirected()).isTrue();
    assertThat(emptyNetwork.allowsSelfLoops()).isTrue();
    assertThat(emptyNetwork.nodeOrder()).isEqualTo(ElementOrder.<String>natural());
  }

  /**

  static <N> EndpointPair<N> of(Graph<?> graph, N nodeU, N nodeV) {
    return graph.isDirected() ? ordered(nodeU, nodeV) : unordered(nodeU, nodeV);
  }

  /** Returns an {@link EndpointPair} representing the endpoints of an edge in {@code network}. */
  static <N> EndpointPair<N> of(Network<?, ?> network, N nodeU, N nodeV) {
    return network.isDirected() ? ordered(nodeU, nodeV) : unordered(nodeU, nodeV);
  }

  /**

        NetworkBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .<String, Integer>immutable()
            .build();

    assertThat(emptyNetwork.isDirected()).isTrue();
    assertThat(emptyNetwork.allowsSelfLoops()).isTrue();
    assertThat(emptyNetwork.nodeOrder()).isEqualTo(ElementOrder.<String>natural());
  }

  /**