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;
  }

 * 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>
 *

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

  private static <N, V> Map<EndpointPair<N>, V> edgeValueMap(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 org.jspecify.annotations.Nullable;

/**
 * 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
 */

  @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

  @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

/**
 * Abstract base class for an incident edges set that allows different implementations of {@link
 * AbstractSet#iterator()}.
 */
abstract class IncidentEdgeSet<N> extends AbstractSet<EndpointPair<N>> {
  final N node;
  final ArchetypeGraph<N> graph;
  final EdgeType edgeType;

  enum EdgeType {
    INCOMING, // incoming incident edges only
    OUTGOING, // outgoing incident edges only

    ValueGraphBuilder<N1, V1> castBuilder = cast();
    return new ImmutableValueGraph.Builder<>(castBuilder);
  }

  /**
   * Specifies whether the graph will allow self-loops (edges that connect a node to itself).
   * Attempting to add a self-loop to a graph that does not allow them will throw an {@link
   * UnsupportedOperationException}.
   *
   * <p>The default value is {@code false}.
   */

    int edgeStart = graphString.indexOf("edges:");
    String nodeString = graphString.substring(nodeStart, edgeStart);

    Network<N, EndpointPair<N>> asNetwork = graph.asNetwork();
    // Don't call AbstractNetworkTest.validateNetwork(asNetwork).  Mutual recursion.
    assertThat(graph.nodes()).isEqualTo(asNetwork.nodes());
    assertThat(graph.edges()).hasSize(asNetwork.edges().size());

 */
@Beta
@DoNotMock("Implement with a lambda, or use GraphBuilder to build a Graph with the desired edges")
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.
   *
   * <p>Some algorithms that operate on a {@code PredecessorsFunction} may produce undesired results