throw new MetadataResolutionException("badly formed edge");
        }
    }
    // ------------------------------------------------------------------------
    public List<MetadataGraphEdge> getEdgesBetween(MetadataGraphVertex vFrom, MetadataGraphVertex vTo) {
        List<MetadataGraphEdge> edges = getIncidentEdges(vTo);
        if (edges == null || edges.isEmpty()) {
            return null;
        }

   * treated as if collapsed into a single edge. For example, the {@link #degree(Object)} of a node
   * in the {@link Graph} view may be less than the degree of the same node in this {@link Network}.
   */
  Graph<N> asGraph();

  //
  // Network properties
  //

  /**
   * Returns true if the edges in this network are directed. Directed edges connect a {@link

  @Test
  public void edges_checkReturnedSetMutability() {
    assume().that(graphIsMutable()).isTrue();

    Set<String> edges = network.edges();
    assertThrows(UnsupportedOperationException.class, () -> edges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.edges()).containsExactlyElementsIn(edges);
  }

  @Override
  @Test
  public void incidentEdges_checkReturnedSetMutability() {

  @Test
  public void edges_checkReturnedSetMutability() {
    assume().that(graphIsMutable()).isTrue();

    Set<String> edges = network.edges();
    assertThrows(UnsupportedOperationException.class, () -> edges.add(E12));
    addEdge(N1, N2, E12);
    assertThat(network.edges()).containsExactlyElementsIn(edges);
  }

  @Override
  @Test
  public void incidentEdges_checkReturnedSetMutability() {

    for (E edge : sanityCheckSet(network.edges())) {
      // TODO(b/27817069): Consider verifying the edge's incident nodes in the string.
      assertThat(edgeString).contains(edge.toString());

      EndpointPair<N> endpointPair = network.incidentNodes(edge);
      N nodeU = endpointPair.nodeU();
      N nodeV = endpointPair.nodeV();
      assertThat(asGraph.edges()).contains(EndpointPair.of(network, nodeU, nodeV));

    for (N node : graph.nodes()) {
      copy.addNode(node);
    }
    for (EndpointPair<N> edge : graph.edges()) {
      copy.putEdge(edge.nodeU(), edge.nodeV());
    }
    return copy;
  }

  /** Creates a mutable copy of {@code graph} with the same nodes, edges, and edge values. */
  public static <N, V> MutableValueGraph<N, V> copyOf(ValueGraph<N, V> graph) {
    MutableValueGraph<N, V> copy =

    for (N node : graph.nodes()) {
      copy.addNode(node);
    }
    for (EndpointPair<N> edge : graph.edges()) {
      copy.putEdge(edge.nodeU(), edge.nodeV());
    }
    return copy;
  }

  /** Creates a mutable copy of {@code graph} with the same nodes, edges, and edge values. */
  public static <N, V> MutableValueGraph<N, V> copyOf(ValueGraph<N, V> graph) {
    MutableValueGraph<N, V> copy =

    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

 *       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

            EndpointPair.ordered(1, 3),
            EndpointPair.ordered(1, 2))
        .inOrder();
  }

  /**
   * Populates the graph with nodes and edges in a star shape with node `1` in the middle.
   *
   * <p>Note that the edges are added in a shuffled order to properly test the effect of the
   * insertion order.
   */
  private void populateStarShapedGraph() {
    putEdge(2, 1);
    putEdge(1, 4);