if (next != null) {
              Iterator<? extends N> successors = successorFunction.successors(next).iterator();
              if (successors.hasNext()) {
                // BFS: horizon.addLast(successors)
                // Pre-order: horizon.addFirst(successors)
                order.insertInto(horizon, successors);
              }
              return next;
            }

  }

  private static final class NodeAndRemainingSuccessors<N> {
    final N node;

    /**
     * The successors left to be visited, or {@code null} if we just added this {@code
     * NodeAndRemainingSuccessors} instance to the stack. In the latter case, we'll compute the
     * successors if we determine that we need them after we've performed the initial processing of
     * the node.
     */

  @Override
  public Set<N> predecessors(N node) {
    return nodeInvalidatableSet(checkedConnections(node).predecessors(), node);
  }

  @Override
  public Set<N> successors(N node) {
    return nodeInvalidatableSet(checkedConnections(node).successors(), node);
  }

  @Override
  public Set<EndpointPair<N>> incidentEdges(N node) {
    GraphConnections<N, V> connections = checkedConnections(node);

      }

      @Override
      public Set<N> predecessors(N node) {
        return AbstractNetwork.this.predecessors(node);
      }

      @Override
      public Set<N> successors(N node) {
        return AbstractNetwork.this.successors(node);
      }

      // DO NOT override the AbstractGraph *degree() implementations.
    };
  }

  @Override
  public int degree(N node) {
    if (isDirected()) {

 * which has a method {@code getChildren()} that retrieves its successors in a graph:
 *
 * {@snippet :
 * someGraphAlgorithm(startNode, MyNode::getChildren);
 * }
 *
 * <p>If you have some other mechanism for returning the successors of a node, or one that doesn't
 * return an {@code Iterable<? extends N>}, then you can use a lambda to perform a more general

   * {@link #edges()}, {@link #adjacentNodes(Object)}, {@link #predecessors(Object)}, {@link
   * #successors(Object)} and {@link #incidentEdges(Object)}.
   *
   * @since 29.0
   */
  @Override
  ElementOrder<N> incidentEdgeOrder();

  //
  // Element-level accessors
  //

  /**
   * Returns a live view of the nodes which have an incident edge in common with {@code node} in

   * {@link #edges()}, {@link #adjacentNodes(Object)}, {@link #predecessors(Object)}, {@link
   * #successors(Object)} and {@link #incidentEdges(Object)}.
   *
   * @since 29.0
   */
  @Override
  ElementOrder<N> incidentEdgeOrder();

  //
  // Element-level accessors
  //

  /**
   * Returns a live view of the nodes which have an incident edge in common with {@code node} in

  @Override
  public Set<N> predecessors(N node) {
    return nodeInvalidatableSet(checkedConnections(node).predecessors(), node);
  }

  @Override
  public Set<N> successors(N node) {
    return nodeInvalidatableSet(checkedConnections(node).successors(), node);
  }

  final NetworkConnections<N, E> checkedConnections(N node) {
    NetworkConnections<N, E> connections = nodeConnections.get(node);
    if (connections == null) {

   *         <li>{@code successors(node)}: Connecting edge insertion order
   *         <li>{@code incidentEdges(node)}: Edge insertion order
   *       </ul>
   *   <li>For {@link Network}:
   *       <ul>
   *         <li>{@code adjacentNodes(node)}: Stable order
   *         <li>{@code predecessors(node)}: Connecting edge insertion order
   *         <li>{@code successors(node)}: Connecting edge insertion order

      }

      @Override
      public Set<N> predecessors(N node) {
        return AbstractValueGraph.this.predecessors(node);
      }

      @Override
      public Set<N> successors(N node) {
        return AbstractValueGraph.this.successors(node);
      }

      @Override
      public int degree(N node) {
        return AbstractValueGraph.this.degree(node);
      }

      @Override