assertThat(graph.nodes()).hasSize(NUM_NODES - numNodesToRemove);
      // Number of edges remaining is unknown (node's incident edges have been removed).
      AbstractGraphTest.validateGraph(graph);

      for (int i = numNodesToRemove; i < NUM_NODES; ++i) {
        assertThat(graph.removeNode(nodeList.get(i))).isTrue();
      }

      assertThat(graph.nodes()).isEmpty();

  /**
   * Returns the subgraph of {@code graph} induced by {@code nodes}. This subgraph is a new graph
   * that contains all of the nodes in {@code nodes}, and all of the {@link Graph#edges() edges}
   * from {@code graph} for which both nodes are contained by {@code nodes}.
   *
   * @throws IllegalArgumentException if any element in {@code nodes} is not a node in the graph
   */

    }
  }

  @Override
  @Test
  public void nodes_checkReturnedSetMutability() {
    Set<Integer> nodes = network.nodes();
    UnsupportedOperationException e =
        assertThrows(UnsupportedOperationException.class, () -> nodes.add(N2));
    addNode(N1);
    assertThat(network.nodes()).containsExactlyElementsIn(nodes);
  }

  @Override
  @Test
  public void edges_checkReturnedSetMutability() {

      @Override
      public Set<N> nodes() {
        return AbstractNetwork.this.nodes();
      }

      @Override
      public Set<EndpointPair<N>> edges() {
        if (allowsParallelEdges()) {
          return super.edges(); // Defer to AbstractGraph implementation.
        }

        // Optimized implementation assumes no parallel edges (1:1 edge to EndpointPair mapping).

    Set<Integer> nodes = network.nodes();
    UnsupportedOperationException e =
        assertThrows(UnsupportedOperationException.class, () -> nodes.add(N2));
    addNode(N1);
    assertThat(network.nodes()).containsExactlyElementsIn(nodes);
  }

  @Override
  @Test
  public void edges_checkReturnedSetMutability() {
    assume().that(graphIsMutable()).isTrue();

    Set<String> edges = network.edges();

  @Override
  public Graph<N> asGraph() {
    return new AbstractGraph<N>() {
      @Override
      public Set<N> nodes() {
        return AbstractValueGraph.this.nodes();
      }

      @Override
      public Set<EndpointPair<N>> edges() {
        return AbstractValueGraph.this.edges();
      }

      @Override
      public boolean isDirected() {
        return AbstractValueGraph.this.isDirected();
      }

    assertThat(graph.nodes()).contains(N1);
  }

  @Test
  public void addNode_existingNode() {
    assume().that(graphIsMutable()).isTrue();

    addNode(N1);
    ImmutableSet<Integer> nodes = ImmutableSet.copyOf(graph.nodes());
    assertThat(graphAsMutableGraph.addNode(N1)).isFalse();
    assertThat(graph.nodes()).containsExactlyElementsIn(nodes);
  }

  @Test

      "Edge %s already exists between the following nodes: %s, "
          + "so it cannot be reused to connect the following nodes: %s.";
  static final String MULTIPLE_EDGES_CONNECTING =
      "Cannot call edgeConnecting() when parallel edges exist between %s and %s. Consider calling "
          + "edgesConnecting() instead.";
  static final String PARALLEL_EDGES_NOT_ALLOWED =

    assertThat(directedGraph.nodes()).isEmpty();
    assertThat(directedGraph.edges()).isEmpty();
    assertThat(directedGraph.addEdge(N1, N2, E12)).isTrue();
    assertThat(directedGraph.edgesConnecting(N1, N2)).isEqualTo(ImmutableSet.of(E12));
    assertThat(directedGraph.edgesConnecting(N2, N1)).isEmpty();

    // By default, parallel edges are not allowed.
    IllegalArgumentException e =

/**
 * Standard implementation of {@link Network} that supports the options supplied by {@link
 * NetworkBuilder}.
 *
 * <p>This class maintains a map of nodes to {@link NetworkConnections}. This class also maintains a
 * map of edges to reference nodes. The reference node is defined to be the edge's source node on
 * directed graphs, and an arbitrary endpoint of the edge on undirected graphs.
 *