@Override
  public N removeInEdge(E edge, boolean isSelfLoop) {
    N node = super.removeInEdge(edge, isSelfLoop);
    Multiset<N> predecessors = getReference(predecessorsReference);
    if (predecessors != null) {
      checkState(predecessors.remove(node));
    }
    return node;
  }

  @Override
  public N removeOutEdge(E edge) {
    N node = super.removeOutEdge(edge);

  // Load factor and capacity for "inner" (i.e. per node/edge element) hash sets or maps
  static final float INNER_LOAD_FACTOR = 1.0f;
  static final int INNER_CAPACITY = 2; // ceiling(EXPECTED_DEGREE / INNER_LOAD_FACTOR)

  // Error messages
  static final String NODE_NOT_IN_GRAPH = "Node %s is not an element of this graph.";
  static final String EDGE_NOT_IN_GRAPH = "Edge %s is not an element of this graph.";

   *     #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

        checkArgument(edges().contains(edge));
        N nodeU = edge.nodeU();
        N nodeV = edge.nodeV();
        Set<EndpointPair<N>> endpointPairIncidentEdges =
            Sets.union(incidentEdges(nodeU), incidentEdges(nodeV));
        return nodePairInvalidatableSet(
            Sets.difference(endpointPairIncidentEdges, ImmutableSet.of(edge)), nodeU, nodeV);
      }

/**
 * 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

    for (E edge : ImmutableList.copyOf(connections.incidentEdges())) {
      removeEdge(edge);
    }
    nodeConnections.remove(node);
    return true;
  }

  @Override
  @CanIgnoreReturnValue
  public boolean removeEdge(E edge) {
    checkNotNull(edge, "edge");

    N nodeU = edgeToReferenceNode.get(edge);
    if (nodeU == null) {
      return false;
    }

 * 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>
 *

                            edge.getTarget() == null
                                    ? null
                                    : edge.getTarget().getMd().getError());
                    MetadataGraphVertex newV = res.addVertex(newMd);
                    MetadataGraphVertex sourceV = res.addVertex(edge.getSource().getMd());

                    res.addEdge(sourceV, newV, edge);
                }
            }

    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}.
   *