*
   * @return the value previously associated with the edge connecting {@code nodeU} to {@code
   *     nodeV}, or null if there was no such edge.
   * @throws IllegalArgumentException if the introduction of the edge would violate {@link
   *     #allowsSelfLoops()}
   */
  @CanIgnoreReturnValue
  @Nullable V putEdgeValue(N nodeU, N nodeV, V value);

  /**

    return (E edge) -> network.incidentNodes(edge).source();
  }

  private static <N, E> Function<E, N> targetNodeFn(Network<N, E> network) {
    return (E edge) -> network.incidentNodes(edge).target();
  }

  private static <N, E> Function<E, N> adjacentNodeFn(Network<N, E> network, N node) {
    return (E edge) -> network.incidentNodes(edge).adjacentNode(node);
  }

  /**

      mutableValueGraph.addNode(node);
      return this;
    }

    /**
     * Adds an edge connecting {@code nodeU} to {@code nodeV} if one is not already present, and
     * sets a value for that edge to {@code value} (overwriting the existing value, if any).
     *
     * <p>If the graph is directed, the resultant edge will be directed; otherwise, it will be
     * undirected.
     *

   *     #allowsSelfLoops()}
   */
  @CanIgnoreReturnValue
  boolean putEdge(N nodeU, N nodeV);

  /**
   * Adds an edge connecting {@code endpoints} (in the order, if any, specified by {@code
   * endpoints}) if one is not already present.
   *
   * <p>If this graph is directed, {@code endpoints} must be ordered and the added edge will be

/**
 * An immutable pair representing the two endpoints of an edge in a graph. The {@link EndpointPair}
 * of a directed edge is an ordered pair of nodes ({@link #source()} and {@link #target()}). The
 * {@link EndpointPair} of an undirected edge is an unordered pair of nodes ({@link #nodeU()} and
 * {@link #nodeV()}).
 *
 * <p>The edge is a self-loop if, and only if, the two endpoints are equal.
 *
 * @author James Sexton

 * and forbids implementations or extensions with parallel edges. If you need parallel edges, use
 * {@link Network}. (You can use a positive {@code Integer} edge value as a loose representation of
 * edge multiplicity, but the {@code *degree()} and mutation methods will not reflect your
 * interpretation of the edge value as its multiplicity.)
 *
 * <h3>Building a {@code ValueGraph}</h3>
 *

    for (N node : graph.nodes()) {
      copy.addNode(node);
    }
    for (EndpointPair<N> edge : graph.edges()) {
      // requireNonNull is safe because the endpoint pair comes from the graph.
      copy.putEdgeValue(
          edge.nodeU(),
          edge.nodeV(),
          requireNonNull(graph.edgeValueOrDefault(edge.nodeU(), edge.nodeV(), null)));
    }
    return copy;
  }

   *     #allowsParallelEdges()} or {@link #allowsSelfLoops()}
   */
  @CanIgnoreReturnValue
  boolean addEdge(N nodeU, N nodeV, E edge);

  /**
   * Adds {@code edge} connecting {@code endpoints}. In an undirected network, {@code edge} will
   * also connect {@code nodeV} to {@code nodeU}.
   *

    public Builder<N> addNode(N node) {
      mutableGraph.addNode(node);
      return this;
    }

    /**
     * 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.
     *

  }

  @Override
  public EndpointPair<N> incidentNodes(E edge) {
    N nodeU = checkedReferenceNode(edge);
    // requireNonNull is safe because checkedReferenceNode made sure the edge is in the network.
    N nodeV = requireNonNull(nodeConnections.get(nodeU)).adjacentNode(edge);
    return EndpointPair.of(this, nodeU, nodeV);
  }

  @Override