@Override
  @Test
  public void outEdges_checkReturnedSetMutability() {
    addNode(N1);
    Set<String> outEdges = network.outEdges(N1);
    assertThrows(UnsupportedOperationException.class, () -> outEdges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.outEdges(N1)).containsExactlyElementsIn(outEdges);
  }

  @Override
  @Test
  public void predecessors_checkReturnedSetMutability() {
    addNode(N2);

        }
      }

      for (E outEdge : sanityCheckSet(network.outEdges(node))) {
        assertThat(network.incidentEdges(node)).contains(outEdge);
        assertThat(network.inEdges(network.incidentNodes(outEdge).adjacentNode(node)))
            .contains(outEdge);
        if (network.isDirected()) {
          assertThat(network.incidentNodes(outEdge).source()).isEqualTo(node);
        }
      }
    }

    assume().that(graphIsMutable()).isTrue();

    addNode(N1);
    Set<String> outEdges = network.outEdges(N1);
    assertThrows(UnsupportedOperationException.class, () -> outEdges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.outEdges(N1)).containsExactlyElementsIn(outEdges);
  }

  @Override
  @Test
  public void predecessors_checkReturnedSetMutability() {

    assume().that(graphIsMutable()).isTrue();

    addNode(N1);
    Set<String> outEdges = network.outEdges(N1);
    assertThrows(UnsupportedOperationException.class, () -> outEdges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.outEdges(N1)).containsExactlyElementsIn(outEdges);
  }

  @Override
  @Test
  public void predecessors_checkReturnedSetMutability() {

  @Override
  @Test
  public void outEdges_checkReturnedSetMutability() {
    addNode(N1);
    Set<String> outEdges = network.outEdges(N1);
    assertThrows(UnsupportedOperationException.class, () -> outEdges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.outEdges(N1)).containsExactlyElementsIn(outEdges);
  }

  @Override
  @Test
  public void predecessors_checkReturnedSetMutability() {
    addNode(N2);

  }

  @Override
  public Set<E> edgesConnecting(N nodeU, N nodeV) {
    Set<E> outEdgesU = outEdges(nodeU);
    Set<E> inEdgesV = inEdges(nodeV);
    return nodePairInvalidatableSet(
        outEdgesU.size() <= inEdgesV.size()
            ? unmodifiableSet(Sets.filter(outEdgesU, connectedPredicate(nodeU, nodeV)))
            : unmodifiableSet(Sets.filter(inEdgesV, connectedPredicate(nodeV, nodeU))),

  }

  @Override
  public Set<E> edgesConnecting(N nodeU, N nodeV) {
    Set<E> outEdgesU = outEdges(nodeU);
    Set<E> inEdgesV = inEdges(nodeV);
    return nodePairInvalidatableSet(
        outEdgesU.size() <= inEdgesV.size()
            ? unmodifiableSet(Sets.filter(outEdgesU, connectedPredicate(nodeU, nodeV)))
            : unmodifiableSet(Sets.filter(inEdgesV, connectedPredicate(nodeV, nodeU))),

  /**
   * Returns a live view of the edges whose {@link #incidentNodes(Object) incident nodes} in this
   * network include {@code node}.
   *
   * <p>This is equal to the union of {@link #inEdges(Object)} and {@link #outEdges(Object)}.
   *
   * <p>If {@code node} is removed from the network after this method is called, the {@code Set}
   * {@code view} returned by this method will be invalidated, and will throw {@code

  /**
   * Returns a live view of the edges whose {@link #incidentNodes(Object) incident nodes} in this
   * network include {@code node}.
   *
   * <p>This is equal to the union of {@link #inEdges(Object)} and {@link #outEdges(Object)}.
   *
   * <p>If {@code node} is removed from the network after this method is called, the {@code Set}
   * {@code view} returned by this method will be invalidated, and will throw {@code

        }

        orderedNodeConnectionsBuilder.add(new NodeConnection.Pred<>(predecessor));
        predecessorCount++;
      } else { // incidentEdge is an outEdge
        checkArgument(incidentEdge.nodeU().equals(thisNode));

        N successor = incidentEdge.nodeV();
        V value = successorNodeToValueFn.apply(successor);