}

  private static SuccessorsFunction<Character> createDirectedGraph(String... edges) {
    return createGraph(/* directed= */ true, edges);
  }

  private static SuccessorsFunction<Character> createUndirectedGraph(String... edges) {
    return createGraph(/* directed= */ false, edges);
  }

  /**
   * Creates a graph from a list of node pairs (encoded as strings, e.g. "ab" means that this graph

   */
  Graph<N> asGraph();

  //
  // ValueGraph properties
  //

  /**
   * Returns true if the edges in this graph are directed. Directed edges connect a {@link
   * EndpointPair#source() source node} to a {@link EndpointPair#target() target node}, while
   * undirected edges connect a pair of nodes to each other.
   */
  @Override

   *
   * <p>If this network is directed, the endpoints must be ordered.
   *
   * @throws IllegalArgumentException if there are multiple parallel edges connecting {@code nodeU}
   *     to {@code nodeV}
   * @throws IllegalArgumentException if either endpoint is not an element of this network
   * @throws IllegalArgumentException if the endpoints are unordered and the network is directed
   * @since 27.1
   */

  /** Returns all edges in this graph. */
  @Override
  Set<EndpointPair<N>> edges();

  //
  // Graph properties
  //

  /**
   * Returns true if the edges in this graph are directed. Directed edges connect a {@link
   * EndpointPair#source() source node} to a {@link EndpointPair#target() target node}, while
   * undirected edges connect a pair of nodes to each other.
   */
  @Override

import java.util.Map;
import java.util.Map.Entry;
import java.util.Set;
import java.util.concurrent.atomic.AtomicBoolean;
import org.jspecify.annotations.Nullable;

/**
 * An implementation of {@link GraphConnections} for directed graphs.
 *
 * @author James Sexton
 * @author Jens Nyman
 * @param <N> Node parameter type
 * @param <V> Value parameter type
 */
final class DirectedGraphConnections<N, V> implements GraphConnections<N, V> {

    return new Traverser<N>(graph) {
      @Override
      Traversal<N> newTraversal() {
        return Traversal.inGraph(graph);
      }
    };
  }

  /**
   * Creates a new traverser for a directed acyclic graph that has at most one path from the start
   * node(s) to any node reachable from the start node(s), and has no paths from any start node to
   * any other start node, such as a tree or forest.
   *

   * starting and ending with the same node.
   *
   * <p>This method will detect any non-empty cycle, including self-loops (a cycle of length 1).
   */
  public static boolean hasCycle(Network<?, ?> network) {
    // In a directed graph, parallel edges cannot introduce a cycle in an acyclic graph.
    // However, in an undirected graph, any parallel edge induces a cycle in the graph.
    if (!network.isDirected()
        && network.allowsParallelEdges()

 *
 * <ul>
 *   <li>Test cases related to whether the graph is directed or undirected.
 *   <li>Test cases related to the specific implementation of the {@link Graph} interface.
 * </ul>
 *
 * TODO(user): Make this class generic (using <N, E>) for all node and edge types.
 * TODO(user): Differentiate between directed and undirected edge strings.
 */
@NullUnmarked
public abstract class AbstractGraphTest {

import java.util.Collections;
import java.util.Optional;
import java.util.Set;
import org.jspecify.annotations.NullUnmarked;
import org.junit.After;
import org.junit.Test;

/**
 * Abstract base class for testing directed {@link Network} implementations defined in this package.
 */
@NullUnmarked
public abstract class AbstractStandardDirectedNetworkTest extends AbstractNetworkTest {

  @After
  public void validateSourceAndTarget() {

import static org.junit.Assert.assertThrows;

import java.util.Set;
import org.jspecify.annotations.NullUnmarked;
import org.junit.Test;

/**
 * Abstract base class for testing directed {@link Graph} implementations defined in this package.
 */
@NullUnmarked
public abstract class AbstractStandardDirectedGraphTest extends AbstractGraphTest {

  @Override
  @Test