diff --git a/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp b/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
index 2e0a0d2703d..1cde09f74c6 100644
--- a/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
+++ b/Polygon_mesh_processing/examples/Polygon_mesh_processing/connected_component.cpp
@@ -47,13 +47,12 @@ int main(int, char* argv[])
 
   std::cerr << cc.size() << " faces in the CC of " << fd << std::endl;
 
-  Mesh::Property_map<face_descriptor,int> fccmap;
-  fccmap = sm.add_property_map<face_descriptor,int>("f:CC").first; 
-  int num = PMP::connected_components(sm,
-                                      fccmap,
-                                      CGAL::parameters::edge_is_constrained_map(Constraint<Mesh>())
-                                      .face_index_map(get(CGAL::face_index, sm))
-                                                                );
+  Mesh::Property_map<face_descriptor,std::size_t> fccmap;
+  fccmap = sm.add_property_map<face_descriptor,std::size_t>("f:CC").first; 
+  std::size_t num = PMP::connected_components(sm,
+                                              fccmap,
+                                              CGAL::parameters::edge_is_constrained_map(Constraint<Mesh>())
+                                              );
   
  std::cerr << "The graph has " << num << " connected components (face connectivity)" << std::endl;
  BOOST_FOREACH(face_descriptor f , faces(sm)){
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
index 44a1f6c20c9..7977cbabc86 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/Connected_components.h
@@ -468,12 +468,14 @@ connected_component(typename boost::graph_traits<PolygonMesh>::face_descriptor s
  *  computes for each face the index of the connected components to which it belongs.
  *  Two faces are considered to be in the same connected component if they share an edge that is not constrained.
  *  \tparam PolygonMesh a model of `FaceGraph`
+ *  \tparam FaceComponentMap the property map with the face descriptor as key type, and the index of its connected component as value type
  *  \tparam EdgeConstraintMap a property map with the edge descriptor as key type and `bool` as value type.
- *  \tparam FaceComponentMap the property map with the face index as value type, and the index of its connected component
+ * \tparam FaceIndexMap a property map for the face index
+ *  \tparam 
  *  \returns the number of connected components.
  */
   template <class PolygonMesh, class EdgeConstraintMap, class FaceComponentMap, class FaceIndexMap>
-typename boost::graph_traits<PolygonMesh>::faces_size_type
+typename boost::property_traits<FaceComponentMap>::value_type
 connected_components(PolygonMesh& pmesh,
                      FaceComponentMap& fcm,
                      EdgeConstraintMap ecmap,
@@ -489,7 +491,7 @@ connected_components(PolygonMesh& pmesh,
 
 
 template <class PolygonMesh, class FaceComponentMap, class P, class T, class R>
-typename boost::graph_traits<PolygonMesh>::faces_size_type
+typename boost::property_traits<FaceComponentMap>::value_type
 connected_components(PolygonMesh& pmesh,
                      FaceComponentMap& fcm,
                      const cgal_bgl_named_params<P,T,R>& params) 
@@ -516,7 +518,7 @@ connected_components(PolygonMesh& pmesh,
  *  \returns the number of connected components.
  */
 template <class PolygonMesh, class FaceComponentMap>
-typename boost::graph_traits<PolygonMesh>::faces_size_type
+typename boost::property_traits<FaceComponentMap>::value_type
 connected_components(PolygonMesh& pmesh,
                      FaceComponentMap& fcm)
 {