* subtype of {@code Network} that provides methods for adding and removing nodes and edges. If you
 * do not need to mutate a network (e.g. if you write a method than runs a read-only algorithm on
 * the network), you should use the non-mutating {@link Network} interface, or an {@link
 * ImmutableNetwork}.
 *
 * <p>You can create an immutable copy of an existing {@code Network} using {@link
 * ImmutableNetwork#copyOf(Network)}:

  public void validateUndirectedEdges() {
    for (Integer node : network.nodes()) {
      new EqualsTester()
          .addEqualityGroup(
              network.inEdges(node), network.outEdges(node), network.incidentEdges(node))
          .testEquals();
      new EqualsTester()
          .addEqualityGroup(
              network.predecessors(node), network.successors(node), network.adjacentNodes(node))
          .testEquals();

    // Edge direction handled correctly
    assertThat(network.outDegree(N2)).isEqualTo(0);
  }

  @Test
  public void edges_selfLoop() {
    assume().that(network.allowsSelfLoops()).isTrue();

    addEdge(N1, N1, E11);
    assertThat(network.edges()).containsExactly(E11);
  }

  @Test
  public void incidentEdges_selfLoop() {

  /**
   * Returns a view of {@code network} with the direction (if any) of every edge reversed. All other
   * properties remain intact, and further updates to {@code network} will be reflected in the view.
   */
  public static <N, E> Network<N, E> transpose(Network<N, E> network) {
    if (!network.isDirected()) {
      return network; // the transpose of an undirected network is an identical network
    }

    return Maps.asMap(network.edges(), network::incidentNodes);
  }

    for (MutableNetwork<Integer, String> network : networksToTest) {
      network.addEdge(1, 2, "1-2a");
      network.addEdge(1, 2, "1-2b");
    }
    assertThat(hasCycle(directedNetwork)).isFalse();
    assertThat(hasCycle(undirectedNetwork)).isTrue(); // cyclic in undirected case
  }

  @Test
  public void hasCycle_cyclicMultigraph() {
    for (MutableNetwork<Integer, String> network : networksToTest) {

   *
   * @return {@code true} if the network was modified as a result of this call
   */
  @CanIgnoreReturnValue
  boolean removeNode(N node);

  /**
   * Removes {@code edge} from this network, if it is present.
   *
   * @return {@code true} if the network was modified as a result of this call
   */
  @CanIgnoreReturnValue
  boolean removeEdge(E edge);

  }

  @Test
  public void copyOfImmutableNetwork_optimized() {
    Network<String, String> network1 =
        ImmutableNetwork.copyOf(NetworkBuilder.directed().<String, String>build());
    Network<String, String> network2 = ImmutableNetwork.copyOf(network1);

    assertThat(network2).isSameInstanceAs(network1);
  }

  @Test
  public void edgesConnecting_directed() {

  @Test
  public void copyOf_directedNetwork() {
    Network<Integer, String> directedGraph = buildDirectedNetwork();

    Network<Integer, String> copy = copyOf(directedGraph);
    assertThat(copy).isEqualTo(directedGraph);
  }

  @Test
  public void copyOf_undirectedNetwork() {
    Network<Integer, String> undirectedGraph = buildUndirectedNetwork();

    Network<Integer, String> copy = copyOf(undirectedGraph);

import static java.util.Objects.requireNonNull;

import com.google.common.collect.ImmutableSet;
import java.util.Map;
import java.util.Set;
import java.util.TreeMap;

/**
 * Standard implementation of {@link Network} that supports the options supplied by {@link
 * NetworkBuilder}.
 *
 * <p>This class maintains a map of nodes to {@link NetworkConnections}. This class also maintains a