// We already know that nodeU equals other.nodeU. Combined with the earlier statement,
        // and the transitive property of equality, this implies that nodeU equals nodeV.
        // If nodeU equals nodeV, condition1 == condition2, so checking condition1 is sufficient.
        return nodeV().equals(other.nodeV());
      }

   *
   * <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 the value previously associated with the edge connecting {@code nodeU} to {@code
   *     nodeV}, or null if there was no such edge.

    GraphConnections<N, V> connectionsU = nodeConnections.get(nodeU);
    return (connectionsU != null) && connectionsU.successors().contains(nodeV);
  }

  private final @Nullable V edgeValueOrDefaultInternal(N nodeU, N nodeV, @Nullable V defaultValue) {
    GraphConnections<N, V> connectionsU = nodeConnections.get(nodeU);
    V value = (connectionsU == null) ? null : connectionsU.value(nodeV);

   * Returns true if there is an edge that directly connects {@code nodeU} to {@code nodeV}. This is
   * equivalent to {@code nodes().contains(nodeU) && successors(nodeU).contains(nodeV)}.
   *
   * <p>In an undirected graph, this is equal to {@code hasEdgeConnecting(nodeV, nodeU)}.
   *
   * @since 23.0
   */
  boolean hasEdgeConnecting(N nodeU, N nodeV);

  /**

   */
  @CanIgnoreReturnValue
  boolean addNode(N node);

  /**
   * Adds an edge connecting {@code nodeU} to {@code nodeV} if one is not already present.
   *
   * <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

   * given nodes is not present in this network.
   *
   * @since 33.1.0
   */
  protected final <T> Set<T> nodePairInvalidatableSet(Set<T> set, N nodeU, N nodeV) {
    return InvalidatableSet.of(
        set,
        () -> nodes().contains(nodeU) && nodes().contains(nodeV),
        () -> String.format(NODE_PAIR_REMOVED_FROM_GRAPH, nodeU, 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();
  }

    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)) {

    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

   * 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