PARALLEL_EDGES_NOT_ALLOWED,
          nodeU,
          nodeV);
    }
    boolean isSelfLoop = nodeU.equals(nodeV);
    if (!allowsSelfLoops()) {
      checkArgument(!isSelfLoop, SELF_LOOPS_NOT_ALLOWED, nodeU);
    }

    if (connectionsU == null) {
      connectionsU = addNodeInternal(nodeU);
    }
    connectionsU.addOutEdge(edge, nodeV);

    // whatever ordering the network's nodes do, so ImmutableSortedMap is unnecessary even if the
    // input nodes are sorted.
    ImmutableMap.Builder<N, NetworkConnections<N, E>> nodeConnections = ImmutableMap.builder();
    for (N node : network.nodes()) {
      nodeConnections.put(node, connectionsOf(network, node));
    }
    return nodeConnections.buildOrThrow();
  }

  public boolean removeNode(N node) {
    return backingValueGraph.removeNode(node);
  }

  @Override
  public boolean removeEdge(N nodeU, N nodeV) {
    return backingValueGraph.removeEdge(nodeU, nodeV) != null;
  }

  @Override
  public boolean removeEdge(EndpointPair<N> endpoints) {
    validateEndpoints(endpoints);
    return removeEdge(endpoints.nodeU(), endpoints.nodeV());
  }

    MutableGraph<N> subgraph =
        (nodes instanceof Collection)
            ? GraphBuilder.from(graph).expectedNodeCount(((Collection) nodes).size()).build()
            : GraphBuilder.from(graph).build();
    for (N node : nodes) {
      subgraph.addNode(node);
    }
    for (N node : subgraph.nodes()) {
      for (N successorNode : graph.successors(node)) {

   * {@code edgeConnectingOrNull(nodeU, nodeV) != null}.
   *
   * <p>In an undirected network, this is equal to {@code hasEdgeConnecting(nodeV, nodeU)}.
   *
   * @since 23.0
   */
  @Override
  boolean hasEdgeConnecting(N nodeU, N nodeV);

  /**
   * Returns true if there is an edge that directly connects {@code endpoints} (in the order, if

   * silently {@link #addNode(Object) add} {@code nodeU} and {@code nodeV} to the graph.
   *
   * <p>If {@code edge} already connects {@code nodeU} to {@code nodeV} (in the specified order if
   * this network {@link #isDirected()}, else in any order), then this method will have no effect.
   *
   * @return {@code true} if the network was modified as a result of this call

      return (node.equals(source) && successorsOrEmpty(node).contains(target))
          || (node.equals(target) && predecessorsOrEmpty(node).contains(source));
    } else {
      Set<N> adjacent = graph.adjacentNodes(node);
      Object nodeU = endpointPair.nodeU();
      Object nodeV = endpointPair.nodeV();

      return (node.equals(nodeV) && adjacent.contains(nodeU))

    checkArgument(containsNode(nodeV), NODE_NOT_IN_GRAPH, nodeV);
    return nodePairInvalidatableSet(connectionsU.edgesConnecting(nodeV), nodeU, nodeV);
  }

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

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

  @Override

     *
     * <p>If the graph is directed, the resultant edge will be directed; otherwise, it will be
     * undirected.
     *
     * <p>If {@code nodeU} and {@code nodeV} are not already present in this graph, this method will
     * silently {@link #addNode(Object) add} {@code nodeU} and {@code nodeV} to the graph.
     *
     * @return this {@code Builder} object

    // whatever ordering the graph's nodes do, so ImmutableSortedMap is unnecessary even if the
    // input nodes are sorted.
    ImmutableMap.Builder<N, GraphConnections<N, V>> nodeConnections = ImmutableMap.builder();
    for (N node : graph.nodes()) {
      nodeConnections.put(node, connectionsOf(graph, node));
    }
    return nodeConnections.buildOrThrow();
  }