/**
   * The undirected graph in the {@link Traverser#breadthFirst(Object)} javadoc:
   *
   * {@snippet :
   * b ---- a ---- d
   * |      |
   * |      |
   * e ---- c ---- f
   * }
   */
  private static final SuccessorsFunction<Character> JAVADOC_GRAPH =
      createUndirectedGraph("ba", "ad", "be", "ac", "ec", "cf");

  /**
   * A diamond shaped directed graph (arrows going down):
   *

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 undirected {@link Network} implementations defined in this
 * package.
 */
@NullUnmarked
public abstract class AbstractStandardUndirectedNetworkTest extends AbstractNetworkTest {

    assertThat(emptyGraph.isDirected()).isTrue();
    assertThat(emptyGraph.allowsSelfLoops()).isTrue();
    assertThat(emptyGraph.nodeOrder()).isEqualTo(ElementOrder.<String>natural());
  }

  @Test
  public void copyOf_incidentEdgeOrder() {
    ImmutableGraph<Object> graph = ImmutableGraph.copyOf(GraphBuilder.undirected().build());

    MutableGraph<Integer> undirectedGraph =
        GraphBuilder.undirected().allowsSelfLoops(false).build();
    undirectedGraph.putEdge(N1, N2);
    undirectedGraph.putEdge(N1, N3);
    undirectedGraph.putEdge(N2, N3);
    undirectedGraph.addNode(N4);

    MutableGraph<Integer> expectedClosure = GraphBuilder.undirected().allowsSelfLoops(true).build();
    expectedClosure.putEdge(N1, N1);

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

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

  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) {

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

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

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

  @Test
  public void directedNetwork() {
    testNetworkMutation(NetworkBuilder.directed());
  }

  @Test
  public void undirectedNetwork() {
    testNetworkMutation(NetworkBuilder.undirected());
  }

  private static void testNetworkMutation(NetworkBuilder<? super Integer, Object> networkBuilder) {

    this.edgeCount = checkNonNegative(edgeCount);
  }

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

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

  @Override
  public boolean allowsSelfLoops() {
    return allowsSelfLoops;
  }

  @Override
  public ElementOrder<N> nodeOrder() {
    return nodeOrder;
  }

    ImmutableValueGraph<String, Integer> emptyGraph =
        ValueGraphBuilder.directed()
            .allowsSelfLoops(true)
            .nodeOrder(ElementOrder.<String>natural())
            .<String, Integer>immutable()
            .build();

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