return nodeConnections.unmodifiableKeySet();
  }

  @Override
  public Set<E> edges() {
    return edgeToReferenceNode.unmodifiableKeySet();
  }

  @Override
  public boolean isDirected() {
    return isDirected;
  }

  @Override
  public boolean allowsParallelEdges() {
    return allowsParallelEdges;
  }

  @Override
  public boolean allowsSelfLoops() {
    return allowsSelfLoops;

   */
  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 =

   */
  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 =

   * interface, such as {@link ValueGraph#isDirected()}. Other properties, such as {@link
   * #expectedNodeCount(int)}, are not set in the new builder.
   */
  public static <N, V> ValueGraphBuilder<N, V> from(ValueGraph<N, V> graph) {
    return new ValueGraphBuilder<N, V>(graph.isDirected())
        .allowsSelfLoops(graph.allowsSelfLoops())
        .nodeOrder(graph.nodeOrder())

   * <p>The "queryable" properties are those that are exposed through the {@link Graph} interface,
   * such as {@link Graph#isDirected()}. Other properties, such as {@link #expectedNodeCount(int)},
   * are not set in the new builder.
   */
  public static <N> GraphBuilder<N> from(Graph<N> graph) {
    return new GraphBuilder<N>(graph.isDirected())
        .allowsSelfLoops(graph.allowsSelfLoops())
        .nodeOrder(graph.nodeOrder())

  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);
  }

  /**

   * such as {@link Network#isDirected()}. Other properties, such as {@link
   * #expectedNodeCount(int)}, are not set in the new builder.
   */
  public static <N, E> NetworkBuilder<N, E> from(Network<N, E> network) {
    return new NetworkBuilder<N, E>(network.isDirected())
        .allowsParallelEdges(network.allowsParallelEdges())

   * interface, such as {@link ValueGraph#isDirected()}. Other properties, such as {@link
   * #expectedNodeCount(int)}, are not set in the new builder.
   */
  public static <N, V> ValueGraphBuilder<N, V> from(ValueGraph<N, V> graph) {
    return new ValueGraphBuilder<N, V>(graph.isDirected())
        .allowsSelfLoops(graph.allowsSelfLoops())
        .nodeOrder(graph.nodeOrder())

  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);
  }

  /**

      requireNonNull(nodeConnections.getWithoutCaching(successor)).removePredecessor(node);
      requireNonNull(connections.removeSuccessor(successor));
      --edgeCount;
    }
    if (isDirected()) { // In undirected graphs, the successor and predecessor sets are equal.
      // Since views are returned, we need to copy the predecessors that will be removed.