ImmutableNetwork<String, Integer> emptyNetwork =
        NetworkBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .<String, Integer>immutable()
            .build();

    assertThat(emptyNetwork.isDirected()).isTrue();
    assertThat(emptyNetwork.allowsSelfLoops()).isTrue();

  /**
   * Returns the node that is adjacent to the origin node along {@code edge}.
   *
   * <p>In the directed case, {@code edge} is assumed to be an outgoing edge.
   */
  N adjacentNode(E edge);

  /**
   * Remove {@code edge} from the set of incoming edges. Returns the former predecessor node.
   *
   * <p>In the undirected case, returns {@code null} if {@code isSelfLoop} is true.
   */
  @CanIgnoreReturnValue

import java.util.Collections;
import java.util.Map;
import java.util.Set;
import org.jspecify.annotations.Nullable;

/**
 * A base implementation of {@link NetworkConnections} for undirected networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
abstract class AbstractUndirectedNetworkConnections<N, E> implements NetworkConnections<N, E> {

 *
 * <ul>
 *   <li>Test cases related to whether the graph is directed, undirected, mutable, or immutable.
 *   <li>Test cases related to the specific implementation of the {@link Network} 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 AbstractNetworkTest {

import java.util.Collections;
import java.util.Map;
import java.util.Set;
import org.jspecify.annotations.Nullable;

/**
 * A base implementation of {@link NetworkConnections} for undirected networks.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
abstract class AbstractUndirectedNetworkConnections<N, E> implements NetworkConnections<N, E> {

  static final String ERROR_ELEMENT_REMOVED = "used to generate this set";
  private static final String NODE_STRING = "Node";
  private static final String EDGE_STRING = "Edge";

  enum EdgeType {
    UNDIRECTED,
    DIRECTED;
  }

  private TestUtil() {}

  static void assertNodeNotInGraphErrorMessage(Throwable throwable) {
    assertThat(throwable).hasMessageThat().startsWith(NODE_STRING);

  private static final int NODE_POOL_SIZE = 1000; // must be >> NUM_NODES

  @Test
  public void directedGraph() {
    testGraphMutation(GraphBuilder.directed());
  }

  @Test
  public void undirectedGraph() {
    testGraphMutation(GraphBuilder.undirected());
  }

  private static void testGraphMutation(GraphBuilder<? super Integer> graphBuilder) {

          + "that allows self-loops, call allowsSelfLoops(true) on the Builder.";
  static final String NOT_AVAILABLE_ON_UNDIRECTED =
      "Cannot call source()/target() on a EndpointPair from an undirected graph. Consider calling "
          + "adjacentNode(node) if you already have a node, or nodeU()/nodeV() if you don't.";
  static final String EDGE_ALREADY_EXISTS = "Edge %s already exists in the graph.";

import java.util.Iterator;
import java.util.LinkedHashMap;
import java.util.Map;
import java.util.Set;
import org.jspecify.annotations.Nullable;

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

import java.util.Collections;
import java.util.HashMap;
import java.util.Map;
import java.util.Set;
import org.jspecify.annotations.Nullable;

/**
 * An implementation of {@link NetworkConnections} for undirected networks with parallel edges.
 *
 * @author James Sexton
 * @param <N> Node parameter type
 * @param <E> Edge parameter type
 */
final class UndirectedMultiNetworkConnections<N, E>