/**
   * Finds the set of clusters which have the strongest "community structure". The more edges
   * removed the smaller and more cohesive the clusters.
   *
   * @param graph the graph
   */
  public Set<Set<V>> transform(Graph<V, E> graph) {

    if (mNumEdgesToRemove < 0 || mNumEdgesToRemove > graph.getEdgeCount()) {
      throw new IllegalArgumentException("Invalid number of edges passed in.");
    }

    edges_removed.clear();

    for (int k = 0; k < mNumEdgesToRemove; k++) {
      BetweennessCentrality<V, E> bc = new BetweennessCentrality<V, E>(graph);
      E to_remove = null;
      double score = 0;
      for (E e : graph.getEdges()) {
        Integer weight = mWeight.get(e);
        if (bc.getEdgeScore(e) / weight > score) {
          to_remove = e;
          score = bc.getEdgeScore(e) / weight;
        }
      }
      edges_removed.put(to_remove, graph.getEndpoints(to_remove));
      graph.removeEdge(to_remove);
    }

    WeakComponentClusterer<V, E> wcSearch = new WeakComponentClusterer<V, E>();
    Set<Set<V>> clusterSet = wcSearch.transform(graph);

    for (Map.Entry<E, Pair<V>> entry : edges_removed.entrySet()) {
      Pair<V> endpoints = entry.getValue();
      graph.addEdge(entry.getKey(), endpoints.getFirst(), endpoints.getSecond());
    }
    return clusterSet;
  }
  private void addEdges() {
    // remove old edges if available
    Iterator<String> e = edgeLabelMap.keySet().iterator();
    while (e.hasNext()) {
      graph.removeEdge(e.next());
    }
    edgeLabelMap.clear();

    boolean isDistance = measure.isDistance();
    Attribute id = exampleSet.getAttributes().getId();
    List<SortableEdge> sortableEdges = new LinkedList<SortableEdge>();
    for (int i = 0; i < exampleSet.size(); i++) {
      Example example = exampleSet.getExample(i);
      for (int j = i + 1; j < exampleSet.size(); j++) {
        Example comExample = exampleSet.getExample(j);
        if (isDistance)
          sortableEdges.add(
              new SortableEdge(
                  example.getValueAsString(id),
                  comExample.getValueAsString(id),
                  null,
                  measure.calculateDistance(example, comExample),
                  SortableEdge.DIRECTION_INCREASE));
        else
          sortableEdges.add(
              new SortableEdge(
                  example.getValueAsString(id),
                  comExample.getValueAsString(id),
                  null,
                  measure.calculateSimilarity(example, comExample),
                  SortableEdge.DIRECTION_DECREASE));
      }
    }

    Collections.sort(sortableEdges);

    int numberOfEdges = distanceSlider.getValue();
    int counter = 0;
    double minStrength = Double.POSITIVE_INFINITY;
    double maxStrength = Double.NEGATIVE_INFINITY;
    Map<String, Double> strengthMap = new HashMap<String, Double>();
    for (SortableEdge sortableEdge : sortableEdges) {
      if (counter > numberOfEdges) break;

      String idString = edgeFactory.create();
      graph.addEdge(
          idString,
          sortableEdge.getFirstVertex(),
          sortableEdge.getSecondVertex(),
          EdgeType.UNDIRECTED);
      edgeLabelMap.put(idString, Tools.formatIntegerIfPossible(sortableEdge.getEdgeValue()));

      double strength = sortableEdge.getEdgeValue();

      minStrength = Math.min(minStrength, strength);
      maxStrength = Math.max(maxStrength, strength);

      strengthMap.put(idString, strength);

      counter++;
    }

    for (Entry<String, Double> entry : strengthMap.entrySet()) {
      edgeStrengthMap.put(
          entry.getKey(), (entry.getValue() - minStrength) / (maxStrength - minStrength));
    }
  }