diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline.h
index 6c5b1f2b039..65343375907 100644
--- a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline.h
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline.h
@@ -16,6 +16,7 @@
 
 #include <CGAL/license/Shape_detection.h>
 
+#include <CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Polyline_graph.h>
 #include <CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/One_ring_neighbor_query.h>
 #include <CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_region.h>
 #include <CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Least_squares_line_fit_sorting.h>
diff --git a/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Polyline_graph.h b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Polyline_graph.h
new file mode 100644
index 00000000000..7f3ecbfb4ed
--- /dev/null
+++ b/Shape_detection/include/CGAL/Shape_detection/Region_growing/Region_growing_on_polyline/Polyline_graph.h
@@ -0,0 +1,107 @@
+// Copyright (c) 2020 GeometryFactory SARL (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Dmitry Anisimov
+//
+
+#ifndef CGAL_SHAPE_DETECTION_REGION_GROWING_POLYLINE_GRAPH_H
+#define CGAL_SHAPE_DETECTION_REGION_GROWING_POLYLINE_GRAPH_H
+
+#include <CGAL/license/Shape_detection.h>
+
+// Boost includes.
+#include <CGAL/boost/graph/named_params_helper.h>
+#include <CGAL/boost/graph/Named_function_parameters.h>
+
+// Internal includes.
+#include <CGAL/Shape_detection/Region_growing/internal/utils.h>
+
+namespace CGAL {
+namespace Shape_detection {
+namespace Polyline {
+
+  template<
+  typename GeomTraits,
+  typename PolygonMesh,
+  typename FaceRange = typename PolygonMesh::Face_range,
+  typename VertexToPointMap = typename boost::property_map<PolygonMesh, CGAL::vertex_point_t>::type>
+  class Polyline_graph {
+
+  public:
+    /// \name Types
+    /// @{
+
+    /// \cond SKIP_IN_MANUAL
+    using Traits = GeomTraits;
+    using Face_graph = PolygonMesh;
+    using Face_range = FaceRange;
+    using Vertex_to_point_map = VertexToPointMap;
+    /// \endcond
+
+    /// Number type.
+    typedef typename GeomTraits::FT FT;
+
+    /// @}
+
+  private:
+    using Point_3 = typename Traits::Point_3;
+    using Vector_3 = typename Traits::Vector_3;
+    using Plane_3 = typename Traits::Plane_3;
+
+    using Squared_length_3 = typename Traits::Compute_squared_length_3;
+    using Squared_distance_3 = typename Traits::Compute_squared_distance_3;
+    using Scalar_product_3 = typename Traits::Compute_scalar_product_3;
+    using Cross_product_3 = typename Traits::Construct_cross_product_vector_3;
+
+  public:
+    template<typename NamedParameters>
+    Polyline_graph(
+      const PolygonMesh& pmesh,
+      const NamedParameters& np,
+      const VertexToPointMap vertex_to_point_map = VertexToPointMap(),
+      const GeomTraits traits = GeomTraits()) :
+    m_face_graph(pmesh),
+    m_face_range(faces(m_face_graph)),
+    m_vertex_to_point_map(vertex_to_point_map),
+    m_squared_length_3(traits.compute_squared_length_3_object()),
+    m_squared_distance_3(traits.compute_squared_distance_3_object()),
+    m_scalar_product_3(traits.compute_scalar_product_3_object()),
+    m_cross_product_3(traits.construct_cross_product_vector_3_object()) {
+
+      CGAL_precondition(m_face_range.size() > 0);
+      m_distance_threshold = parameters::choose_parameter(
+        parameters::get_parameter(np, internal_np::distance_threshold), FT(1));
+      CGAL_precondition(m_distance_threshold >= FT(0));
+    }
+
+  private:
+    const Face_graph& m_face_graph;
+    const Face_range m_face_range;
+
+    FT m_distance_threshold;
+    FT m_cos_value_threshold;
+    std::size_t m_min_region_size;
+
+    const Vertex_to_point_map m_vertex_to_point_map;
+
+    const Squared_length_3 m_squared_length_3;
+    const Squared_distance_3 m_squared_distance_3;
+    const Scalar_product_3 m_scalar_product_3;
+    const Cross_product_3 m_cross_product_3;
+
+    Plane_3 m_plane_of_best_fit;
+    Vector_3 m_normal_of_best_fit;
+  };
+
+} // namespace Polyline
+} // namespace Shape_detection
+} // namespace CGAL
+
+#endif // CGAL_SHAPE_DETECTION_REGION_GROWING_POLYLINE_GRAPH_H