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

  /**
   * Defer to {@link AbstractValueGraph#edges()} (based on {@link #successors(Object)}) for full
   * edges() implementation.
   */
  @Override
  protected long edgeCount() {
    return delegate().edges().size();
  }

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

  @Override

        + nodes()
        + ", edges: "
        + edgeValueMap(this);
  }

  private static <N, V> Map<EndpointPair<N>, V> edgeValueMap(final ValueGraph<N, V> graph) {
    return Maps.asMap(
        graph.edges(),
        edge ->
            // requireNonNull is safe because the endpoint pair comes from the graph.
            requireNonNull(graph.edgeValueOrDefault(edge.nodeU(), edge.nodeV(), null)));
  }

import javax.annotation.CheckForNull;

/**
 * A class to represent the set of edges connecting an (implicit) origin node to a target node.
 *
 * <p>The {@link #outEdgeToNode} map allows this class to work on networks with parallel edges. See
 * {@link EdgesConnecting} for a class that is more efficient but forbids parallel edges.
 *
 * @author James Sexton
 * @param <E> Edge parameter type
 */
@ElementTypesAreNonnullByDefault

@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
@ElementTypesAreNonnullByDefault
public interface PredecessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s incoming edges <i>against</i> the direction (if any) of the edge.
   *

 * user-defined properties.
 *
 * <p>A {@code Network} built by this class has the following default properties:
 *
 * <ul>
 *   <li>does not allow parallel edges
 *   <li>does not allow self-loops
 *   <li>orders {@link Network#nodes()} and {@link Network#edges()} in the order in which the
 *       elements were added (insertion order)
 * </ul>
 *

            EndpointPair.unordered(1, 1),
            EndpointPair.unordered(1, 3))
        .inOrder();
  }

  /**
   * Populates the graph with nodes and edges in a star shape with node `1` in the middle.
   *
   * <p>Note that the edges are added in a shuffled order to properly test the effect of the
   * insertion order.
   */
  private void populateTShapedGraph() {
    putEdge(2, 1);
    putEdge(1, 4);

    ImmutableValueGraph<String, Integer> graph =
        ValueGraphBuilder.directed().<String, Integer>immutable().addNode("A").build();

    assertThat(graph.nodes()).containsExactly("A");
    assertThat(graph.edges()).isEmpty();
  }

  @Test
  public void immutableValueGraphBuilder_putEdgeFromNodes() {
    ImmutableValueGraph<String, Integer> graph =
        ValueGraphBuilder.directed()

  Optional<Integer> expectedNodeCount = Optional.absent();

  /**
   * Creates a new instance with the specified edge directionality.
   *
   * @param directed if true, creates an instance for graphs whose edges are each directed; if
   *     false, creates an instance for graphs whose edges are each undirected.
   */
  AbstractGraphBuilder(boolean directed) {
    this.directed = directed;
  }

@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
@ElementTypesAreNonnullByDefault
public interface PredecessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s incoming edges <i>against</i> the direction (if any) of the edge.
   *

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

  /**
   * Defer to {@link AbstractGraph#edges()} (based on {@link #successors(Object)}) for full edges()
   * implementation.
   */
  @Override
  protected long edgeCount() {
    return delegate().edges().size();
  }

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

  @Override