return false;
    }
    Graph<?> other = (Graph<?>) obj;

    return isDirected() == other.isDirected()
        && nodes().equals(other.nodes())
        && edges().equals(other.edges());
  }

  @Override
  public final int hashCode() {
    return edges().hashCode();
  }

  /** Returns a string representation of this graph. */
  @Override
  public String toString() {
    return "isDirected: "

/**
 * 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

public interface SuccessorsFunction<N> {

  /**
   * Returns all nodes in this graph adjacent to {@code node} which can be reached by traversing
   * {@code node}'s outgoing edges in the direction (if any) of the edge.
   *
   * <p>This is <i>not</i> the same as "all nodes reachable from {@code node} by following outgoing

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 #nodeToOutEdge} map means this class only works on networks without parallel edges.
 * See {@link MultiEdgesConnecting} for a class that works with parallel edges.
 *
 * @author James Sexton
 * @param <E> Edge parameter type
 */
final class EdgesConnecting<E> extends AbstractSet<E> {

        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);
      }

    ImmutableSet<String> edges = ImmutableSet.copyOf(network.edges());
    assertThat(networkAsMutableNetwork.addEdge(N1, N2, E12)).isFalse();
    assertThat(network.edges()).containsExactlyElementsIn(edges);
    assertThat(networkAsMutableNetwork.addEdge(N2, N1, E12)).isFalse();
    assertThat(network.edges()).containsExactlyElementsIn(edges);
  }

  @Test

 */
@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

        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).
        return new AbstractSet<EndpointPair<N>>() {
          @Override

        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).
        return new AbstractSet<EndpointPair<N>>() {
          @Override

 *       locks---to each of the acquired locks, an edge from the soon-to-be-acquired lock is either
 *       verified or created.
 *   <li>If a new edge needs to be created, the outgoing edges of the acquired locks are traversed
 *       to check for a cycle that reaches the lock to be acquired. If no cycle is detected, a new
 *       "safe" edge is created.
 *   <li>If a cycle is detected, an "unsafe" (cyclic) edge is created to represent a potential