示例#1
0
  private SimpleGraph<Integer, DefaultEdge> buildGraphForTestDisconnected(int size) {
    SimpleGraph<Integer, DefaultEdge> graph = new SimpleGraph<>(DefaultEdge.class);

    VertexFactory<Integer> vertexFactory = new IntegerVertexFactory();

    CompleteGraphGenerator<Integer, DefaultEdge> completeGraphGenerator =
        new CompleteGraphGenerator<>(size);
    // two complete graphs
    SimpleGraph<Integer, DefaultEdge> east = new SimpleGraph<>(DefaultEdge.class);
    completeGraphGenerator.generateGraph(east, vertexFactory, null);

    SimpleGraph<Integer, DefaultEdge> west = new SimpleGraph<>(DefaultEdge.class);
    completeGraphGenerator.generateGraph(west, vertexFactory, null);

    Graphs.addGraph(graph, east);
    Graphs.addGraph(graph, west);
    // connected by single edge
    graph.addEdge(size - 1, size);

    return graph;
  }
示例#2
0
  /**
   * Testing a graph where the validator denies the request to go on an edge which cutting it makes
   * the graph disconnected
   */
  public void testDisconnected() {
    int cliqueSize = 5;
    // generate graph of two cliques connected by single edge
    SimpleGraph<Integer, DefaultEdge> graph = buildGraphForTestDisconnected(cliqueSize);
    for (int i = 0; i < graph.vertexSet().size(); i++) {
      KShortestPaths<Integer, DefaultEdge> ksp =
          new KShortestPaths<Integer, DefaultEdge>(
              graph,
              i,
              100,
              Integer.MAX_VALUE,
              new PathValidator<Integer, DefaultEdge>() {

                @Override
                public boolean isValidPath(
                    AbstractPathElement<Integer, DefaultEdge> prevPathElement, DefaultEdge edge) {
                  // accept all requests but the one to pass through the edge connecting
                  // the two cliques.
                  DefaultEdge connectingEdge = graph.getEdge(cliqueSize - 1, cliqueSize);
                  return connectingEdge != edge;
                }
              });

      for (int j = 0; j < graph.vertexSet().size(); j++) {
        if (j == i) {
          continue;
        }
        List<GraphPath<Integer, DefaultEdge>> paths = ksp.getPaths(j);
        if ((i < cliqueSize && j < cliqueSize) || (i >= cliqueSize && j >= cliqueSize)) {
          // within the clique - path should exist
          assertNotNull(paths);
          assertTrue(paths.size() > 0);
        } else {
          // else - should not
          assertNull(paths);
        }
      }
    }
  }
  /** SEM Tests the edge- and vertex-comparator */
  @Test
  public void testSemanticCheck() {

    /*
     *       a---<3>---b
     *       |         |
     * g1 = <4>       <1>   g2 = A---<6>---b---<5>---B
     *       |         |
     *       A---<2>---B
     */

    SimpleGraph<String, Integer> g1 = new SimpleGraph<>(Integer.class),
        g2 = new SimpleGraph<>(Integer.class);

    g1.addVertex("a");
    g1.addVertex("b");
    g1.addVertex("A");
    g1.addVertex("B");

    g1.addEdge("a", "b", 3);
    g1.addEdge("b", "B", 1);
    g1.addEdge("B", "A", 2);
    g1.addEdge("A", "a", 4);

    g2.addVertex("A");
    g2.addVertex("b");
    g2.addVertex("B");

    g2.addEdge("A", "b", 6);
    g2.addEdge("b", "B", 5);

    /* SEM-1
     * test vertex and edge comparator */

    VF2SubgraphIsomorphismInspector<String, Integer> vf2 =
        new VF2SubgraphIsomorphismInspector<>(g1, g2, new VertexComp(), new EdgeComp());

    Iterator<GraphMapping<String, Integer>> iter = vf2.getMappings();

    assertEquals("[A=A B=b a=~~ b=B]", iter.next().toString());
    assertEquals(false, iter.hasNext());

    /* SEM-2
     * test vertex comparator */

    VF2SubgraphIsomorphismInspector<String, Integer> vf3 =
        new VF2SubgraphIsomorphismInspector<>(
            g1, g2, new VertexComp(), new AlwaysEqualComparator<>());

    Iterator<GraphMapping<String, Integer>> iter2 = vf3.getMappings();

    Set<String> mappings = new HashSet<>(Arrays.asList("[A=A B=b a=~~ b=B]", "[A=~~ B=B a=A b=b]"));
    assertEquals(true, mappings.remove(iter2.next().toString()));
    assertEquals(true, mappings.remove(iter2.next().toString()));
    assertEquals(false, iter2.hasNext());

    /* SEM-3
     * test edge comparator */

    VF2SubgraphIsomorphismInspector<String, Integer> vf4 =
        new VF2SubgraphIsomorphismInspector<>(
            g1, g2, new AlwaysEqualComparator<>(), new EdgeComp());

    Iterator<GraphMapping<String, Integer>> iter3 = vf4.getMappings();

    Set<String> mappings2 =
        new HashSet<>(Arrays.asList("[A=A B=b a=~~ b=B]", "[A=A B=~~ a=b b=B]"));
    assertEquals(true, mappings2.remove(iter3.next().toString()));
    assertEquals(true, mappings2.remove(iter3.next().toString()));
    assertEquals(false, iter3.hasNext());
  }
  @Test
  public void testExhaustive() {

    /* DET-1:
     *
     *      0   3
     *      |  /|        0 2
     * g1 = | 2 |   g2 = |/
     *      |/  |        1
     *      1   4
     */

    SimpleGraph<Integer, DefaultEdge> g1 = new SimpleGraph<>(DefaultEdge.class),
        g2 = new SimpleGraph<>(DefaultEdge.class);

    g1.addVertex(0);
    g1.addVertex(1);
    g1.addVertex(2);
    g1.addVertex(3);
    g1.addVertex(4);

    g2.addVertex(0);
    g2.addVertex(1);
    g2.addVertex(2);

    g1.addEdge(0, 1);
    g1.addEdge(1, 2);
    g1.addEdge(2, 3);
    g1.addEdge(3, 4);

    g2.addEdge(0, 1);
    g2.addEdge(1, 2);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vf2 =
        new VF2SubgraphIsomorphismInspector<>(g1, g2);

    assertEquals(true, SubgraphIsomorphismTestUtils.containsAllMatchings(vf2, g1, g2));

    /* DET-2:
     *
     * g3 = ...   g4 = ...
     *
     */

    DirectedGraph<Integer, DefaultEdge> g3 = new DefaultDirectedGraph<>(DefaultEdge.class),
        g4 = new DefaultDirectedGraph<>(DefaultEdge.class);

    g3.addVertex(0);
    g3.addVertex(1);
    g3.addVertex(2);
    g3.addVertex(3);
    g3.addVertex(4);
    g3.addVertex(5);

    g4.addVertex(0);
    g4.addVertex(1);
    g4.addVertex(2);
    g4.addVertex(3);

    g3.addEdge(0, 1);
    g3.addEdge(0, 5);
    g3.addEdge(1, 4);
    g3.addEdge(2, 1);
    g3.addEdge(2, 4);
    g3.addEdge(3, 1);
    g3.addEdge(4, 0);
    g3.addEdge(5, 2);
    g3.addEdge(5, 4);

    g4.addEdge(0, 3);
    g4.addEdge(1, 2);
    g4.addEdge(1, 3);
    g4.addEdge(2, 3);
    g4.addEdge(2, 0);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vf3 =
        new VF2SubgraphIsomorphismInspector<>(g3, g4);

    assertEquals(true, SubgraphIsomorphismTestUtils.containsAllMatchings(vf3, g3, g4));

    /* DET-3:
     *
     *      1----0        0---2
     *      |             |  /
     * g5 = |        g6 = | /
     *      |             |/
     *      2----3        1
     */

    SimpleGraph<Integer, DefaultEdge> g5 = new SimpleGraph<>(DefaultEdge.class),
        g6 = new SimpleGraph<>(DefaultEdge.class);

    g5.addVertex(0);
    g5.addVertex(1);
    g5.addVertex(2);
    g5.addVertex(3);

    g6.addVertex(0);
    g6.addVertex(1);
    g6.addVertex(2);

    g5.addEdge(0, 1);
    g5.addEdge(1, 2);
    g5.addEdge(2, 3);

    g6.addEdge(0, 1);
    g6.addEdge(1, 2);
    g6.addEdge(2, 0);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vf4 =
        new VF2SubgraphIsomorphismInspector<>(g5, g6);

    assertEquals(true, SubgraphIsomorphismTestUtils.containsAllMatchings(vf4, g5, g6));
  }
  /**
   * Tests graph types: In case of invalid graph types or invalid combination of graph arguments
   * UnsupportedOperationException or InvalidArgumentException is expected
   */
  @Test
  public void testGraphTypes() {

    DirectedGraph<Integer, DefaultEdge> dg1 = new DefaultDirectedGraph<>(DefaultEdge.class);

    dg1.addVertex(1);
    dg1.addVertex(2);

    dg1.addEdge(1, 2);

    SimpleGraph<Integer, DefaultEdge> sg1 = new SimpleGraph<>(DefaultEdge.class);

    sg1.addVertex(1);
    sg1.addVertex(2);

    sg1.addEdge(1, 2);

    Multigraph<Integer, DefaultEdge> mg1 = new Multigraph<>(DefaultEdge.class);

    mg1.addVertex(1);
    mg1.addVertex(2);

    mg1.addEdge(1, 2);

    Pseudograph<Integer, DefaultEdge> pg1 = new Pseudograph<>(DefaultEdge.class);

    pg1.addVertex(1);
    pg1.addVertex(2);

    pg1.addEdge(1, 2);

    /* GT-0 test graph=null */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt0 =
          new VF2SubgraphIsomorphismInspector<>(null, sg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (NullPointerException ex) {
    }

    /* GT-1: multigraphs */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt1 =
          new VF2SubgraphIsomorphismInspector<>(mg1, mg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-2: pseudographs */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt2 =
          new VF2SubgraphIsomorphismInspector<>(pg1, pg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-3: simple graphs */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt3 =
        new VF2SubgraphIsomorphismInspector<>(sg1, sg1);
    assertEquals(true, gt3.getMappings().hasNext());

    /* GT-4: directed graphs */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt4 =
        new VF2SubgraphIsomorphismInspector<>(dg1, dg1);
    assertEquals("[1=1 2=2]", gt4.getMappings().next().toString());

    /* GT-5: simple graph + multigraph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt5 =
          new VF2SubgraphIsomorphismInspector<>(sg1, mg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-6: simple graph + pseudograph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt6 =
          new VF2SubgraphIsomorphismInspector<>(sg1, pg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-7: directed graph + multigraph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt7 =
          new VF2SubgraphIsomorphismInspector<>(dg1, mg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-8: directed graph + pseudograph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt8 =
          new VF2SubgraphIsomorphismInspector<>(dg1, pg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-9: pseudograph + multigraph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt9 =
          new VF2SubgraphIsomorphismInspector<>(pg1, mg1);
      Assert.fail("Expected UnsupportedOperationException");
    } catch (UnsupportedOperationException ex) {
    }

    /* GT-10: simple graph + directed graph */

    try {
      @SuppressWarnings("unused")
      VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> gt10 =
          new VF2SubgraphIsomorphismInspector<>(sg1, dg1);
      Assert.fail("Expected IllegalArgumentException");
    } catch (IllegalArgumentException ex) {
    }
  }
  /** Tests edge cases on simple graphs */
  @Test
  public void testEdgeCasesSimpleGraph() {

    /* ECS-1: graph and subgraph empty */

    SimpleGraph<Integer, DefaultEdge> sg0v = new SimpleGraph<>(DefaultEdge.class),
        sg0v2 = new SimpleGraph<>(DefaultEdge.class);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs1 =
        new VF2SubgraphIsomorphismInspector<>(sg0v, sg0v2);

    assertEquals("[]", vfs1.getMappings().next().toString());

    /* ECS-2: graph non-empty, subgraph empty */

    SimpleGraph<Integer, DefaultEdge> sg4v3e = new SimpleGraph<>(DefaultEdge.class);

    sg4v3e.addVertex(1);
    sg4v3e.addVertex(2);
    sg4v3e.addVertex(3);
    sg4v3e.addVertex(4);

    sg4v3e.addEdge(1, 2);
    sg4v3e.addEdge(3, 2);
    sg4v3e.addEdge(3, 4);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs2 =
        new VF2SubgraphIsomorphismInspector<>(sg4v3e, sg0v);

    assertEquals("[1=~~ 2=~~ 3=~~ 4=~~]", vfs2.getMappings().next().toString());

    /* ECS-3: graph empty, subgraph non-empty */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs3 =
        new VF2SubgraphIsomorphismInspector<>(sg0v, sg4v3e);

    assertEquals(false, vfs3.isomorphismExists());

    /* ECS-4: graph non-empty, subgraph single vertex */

    SimpleGraph<Integer, DefaultEdge> sg1v = new SimpleGraph<>(DefaultEdge.class);

    sg1v.addVertex(5);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs4 =
        new VF2SubgraphIsomorphismInspector<>(sg4v3e, sg1v);

    Iterator<GraphMapping<Integer, DefaultEdge>> iter = vfs4.getMappings();

    Set<String> mappings =
        new HashSet<>(
            Arrays.asList(
                "[1=5 2=~~ 3=~~ 4=~~]",
                "[1=~~ 2=5 3=~~ 4=~~]",
                "[1=~~ 2=~~ 3=5 4=~~]",
                "[1=~~ 2=~~ 3=~~ 4=5]"));
    assertEquals(true, mappings.remove(iter.next().toString()));
    assertEquals(true, mappings.remove(iter.next().toString()));
    assertEquals(true, mappings.remove(iter.next().toString()));
    assertEquals(true, mappings.remove(iter.next().toString()));
    assertEquals(false, iter.hasNext());

    /* ECS-5: graph empty, subgraph single vertex */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs5 =
        new VF2SubgraphIsomorphismInspector<>(sg0v, sg1v);

    assertEquals(false, vfs5.isomorphismExists());

    /* ECS-6: subgraph with vertices, but no edges */

    SimpleGraph<Integer, DefaultEdge> sg3v0e = new SimpleGraph<>(DefaultEdge.class);

    sg3v0e.addVertex(5);
    sg3v0e.addVertex(6);
    sg3v0e.addVertex(7);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs6 =
        new VF2SubgraphIsomorphismInspector<>(sg4v3e, sg3v0e);

    assertEquals(false, vfs6.isomorphismExists());

    /* ECS-7: graph and subgraph with vertices, but no edges */

    SimpleGraph<Integer, DefaultEdge> sg2v0e = new SimpleGraph<>(DefaultEdge.class);

    sg2v0e.addVertex(1);
    sg2v0e.addVertex(2);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs7 =
        new VF2SubgraphIsomorphismInspector<>(sg3v0e, sg2v0e);

    Iterator<GraphMapping<Integer, DefaultEdge>> iter7 = vfs7.getMappings();

    Set<String> mappings7 =
        new HashSet<>(
            Arrays.asList(
                "[5=1 6=2 7=~~]",
                "[5=1 6=~~ 7=2]",
                "[5=2 6=1 7=~~]",
                "[5=~~ 6=1 7=2]",
                "[5=2 6=~~ 7=1]",
                "[5=~~ 6=2 7=1]"));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(true, mappings7.remove(iter7.next().toString()));
    assertEquals(false, iter7.hasNext());

    /* ECS-8: graph no edges, subgraph contains single edge */

    SimpleGraph<Integer, DefaultEdge> sg2v1e = new SimpleGraph<>(DefaultEdge.class);

    sg2v1e.addVertex(5);
    sg2v1e.addVertex(6);

    sg2v1e.addEdge(5, 6);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs8 =
        new VF2SubgraphIsomorphismInspector<>(sg3v0e, sg2v1e);

    assertEquals(false, vfs8.isomorphismExists());

    /* ECS-9: complete graphs of different size,
     * graph smaller than subgraph */

    SimpleGraph<Integer, DefaultEdge> sg5k = new SimpleGraph<>(DefaultEdge.class);

    sg5k.addVertex(0);
    sg5k.addVertex(1);
    sg5k.addVertex(2);
    sg5k.addVertex(3);
    sg5k.addVertex(4);

    sg5k.addEdge(0, 1);
    sg5k.addEdge(0, 2);
    sg5k.addEdge(0, 3);
    sg5k.addEdge(0, 4);
    sg5k.addEdge(1, 2);
    sg5k.addEdge(1, 3);
    sg5k.addEdge(1, 4);
    sg5k.addEdge(2, 3);
    sg5k.addEdge(2, 4);
    sg5k.addEdge(3, 4);

    SimpleGraph<Integer, DefaultEdge> sg4k = new SimpleGraph<>(DefaultEdge.class);

    sg4k.addVertex(0);
    sg4k.addVertex(1);
    sg4k.addVertex(2);
    sg4k.addVertex(3);

    sg4k.addEdge(0, 1);
    sg4k.addEdge(0, 2);
    sg4k.addEdge(0, 3);
    sg4k.addEdge(1, 2);
    sg4k.addEdge(1, 3);
    sg4k.addEdge(2, 3);

    SimpleGraph<Integer, DefaultEdge> sg3k = new SimpleGraph<>(DefaultEdge.class);

    sg3k.addVertex(0);
    sg3k.addVertex(1);
    sg3k.addVertex(2);

    sg3k.addEdge(0, 1);
    sg3k.addEdge(0, 2);
    sg3k.addEdge(1, 2);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs9 =
        new VF2SubgraphIsomorphismInspector<>(sg4k, sg5k);

    assertEquals(false, vfs9.isomorphismExists());

    /* ECS-10: complete graphs of different size,
     * graph bigger than subgraph */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs10 =
        new VF2SubgraphIsomorphismInspector<>(sg4k, sg3k);
    Iterator<GraphMapping<Integer, DefaultEdge>> iter10 = vfs10.getMappings();

    Set<String> mappings10 =
        new HashSet<>(
            Arrays.asList(
                "[0=0 1=1 2=2 3=~~]",
                "[0=0 1=1 2=~~ 3=2]",
                "[0=0 1=~~ 2=1 3=2]",
                "[0=~~ 1=0 2=1 3=2]",
                "[0=1 1=0 2=2 3=~~]",
                "[0=1 1=0 2=~~ 3=2]",
                "[0=1 1=~~ 2=0 3=2]",
                "[0=~~ 1=1 2=0 3=2]",
                "[0=2 1=1 2=0 3=~~]",
                "[0=2 1=1 2=~~ 3=0]",
                "[0=2 1=~~ 2=1 3=0]",
                "[0=~~ 1=2 2=1 3=0]",
                "[0=0 1=2 2=1 3=~~]",
                "[0=0 1=2 2=~~ 3=1]",
                "[0=0 1=~~ 2=2 3=1]",
                "[0=~~ 1=0 2=2 3=1]",
                "[0=1 1=2 2=0 3=~~]",
                "[0=1 1=2 2=~~ 3=0]",
                "[0=1 1=~~ 2=2 3=0]",
                "[0=~~ 1=1 2=2 3=0]",
                "[0=2 1=0 2=1 3=~~]",
                "[0=2 1=0 2=~~ 3=1]",
                "[0=2 1=~~ 2=0 3=1]",
                "[0=~~ 1=2 2=0 3=1]"));
    for (int i = 0; i < 24; i++) assertEquals(true, mappings10.remove(iter10.next().toString()));
    assertEquals(false, iter10.hasNext());

    /* ECS-11: isomorphic graphs */

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs11 =
        new VF2SubgraphIsomorphismInspector<>(sg4v3e, sg4v3e);

    Iterator<GraphMapping<Integer, DefaultEdge>> iter11 = vfs11.getMappings();

    Set<String> mappings11 = new HashSet<>(Arrays.asList("[1=1 2=2 3=3 4=4]", "[1=4 2=3 3=2 4=1]"));
    assertEquals(true, mappings11.remove(iter11.next().toString()));
    assertEquals(true, mappings11.remove(iter11.next().toString()));
    assertEquals(false, iter11.hasNext());

    /* ECS-12: not connected graphs of different size */

    SimpleGraph<Integer, DefaultEdge> sg6v4enc = new SimpleGraph<>(DefaultEdge.class);

    sg6v4enc.addVertex(0);
    sg6v4enc.addVertex(1);
    sg6v4enc.addVertex(2);
    sg6v4enc.addVertex(3);
    sg6v4enc.addVertex(4);
    sg6v4enc.addVertex(5);

    sg6v4enc.addEdge(1, 2);
    sg6v4enc.addEdge(2, 3);
    sg6v4enc.addEdge(3, 1);
    sg6v4enc.addEdge(4, 5);

    SimpleGraph<Integer, DefaultEdge> sg5v4enc = new SimpleGraph<>(DefaultEdge.class);

    sg5v4enc.addVertex(6);
    sg5v4enc.addVertex(7);
    sg5v4enc.addVertex(8);
    sg5v4enc.addVertex(9);
    sg5v4enc.addVertex(10);

    sg5v4enc.addEdge(7, 6);
    sg5v4enc.addEdge(9, 8);
    sg5v4enc.addEdge(10, 9);
    sg5v4enc.addEdge(8, 10);

    VF2SubgraphIsomorphismInspector<Integer, DefaultEdge> vfs12 =
        new VF2SubgraphIsomorphismInspector<>(sg6v4enc, sg5v4enc);

    Iterator<GraphMapping<Integer, DefaultEdge>> iter12 = vfs12.getMappings();

    Set<String> mappings12 =
        new HashSet<>(
            Arrays.asList(
                "[0=~~ 1=8 2=10 3=9 4=7 5=6]",
                "[0=~~ 1=9 2=8 3=10 4=7 5=6]",
                "[0=~~ 1=10 2=9 3=8 4=7 5=6]",
                "[0=~~ 1=8 2=10 3=9 4=6 5=7]",
                "[0=~~ 1=9 2=8 3=10 4=6 5=7]",
                "[0=~~ 1=10 2=9 3=8 4=6 5=7]",
                "[0=~~ 1=10 2=8 3=9 4=7 5=6]",
                "[0=~~ 1=8 2=9 3=10 4=7 5=6]",
                "[0=~~ 1=9 2=10 3=8 4=7 5=6]",
                "[0=~~ 1=10 2=8 3=9 4=6 5=7]",
                "[0=~~ 1=8 2=9 3=10 4=6 5=7]",
                "[0=~~ 1=9 2=10 3=8 4=6 5=7]"));
    for (int i = 0; i < 12; i++) assertEquals(true, mappings12.remove(iter12.next().toString()));
    assertEquals(false, iter12.hasNext());
  }