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diff --git a/src/Alpha_complex/test/Delaunay_complex_unit_test.h b/src/Alpha_complex/test/Delaunay_complex_unit_test.h
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+++ b/src/Alpha_complex/test/Delaunay_complex_unit_test.h
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+/*    This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
+ *    See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
+ *    Author(s):       Vincent Rouvreau
+ *
+ *    Copyright (C) 2020 Inria
+ *
+ *    Modification(s):
+ *      - YYYY/MM Author: Description of the modification
+ */
+
+#include <vector>
+#include <limits>  // NaN
+#include <cmath>
+
+#include <gudhi/Alpha_complex.h>
+// to construct a simplex_tree from Delaunay_triangulation
+#include <gudhi/graph_simplicial_complex.h>
+#include <gudhi/Simplex_tree.h>
+#include <gudhi/Unitary_tests_utils.h>
+#include <gudhi/random_point_generators.h>
+
+using Simplex_tree = Gudhi::Simplex_tree<>;
+using Simplex_handle = Simplex_tree::Simplex_handle;
+
+template<class CGAL_kernel>
+void compare_delaunay_complex_simplices() {
+  std::cout << "*****************************************************************************************************";
+  using Point = typename CGAL_kernel::Point_d;
+  std::vector<Point> points;
+  // 50 points on a 4-sphere
+  points = Gudhi::generate_points_on_sphere_d<CGAL_kernel>(10, 5, 1.);
+
+  Gudhi::alpha_complex::Alpha_complex<CGAL_kernel> alpha_complex(points);
+
+  // Alpha complex
+  Simplex_tree stree_from_alpha_complex;
+  BOOST_CHECK(alpha_complex.create_complex(stree_from_alpha_complex));
+
+  // Delaunay complex
+  Simplex_tree stree_from_delaunay_complex;
+  BOOST_CHECK(alpha_complex.create_complex(stree_from_delaunay_complex, 0., false, true));
+
+  // Check all the simplices from alpha complex are in the Delaunay complex
+  for (auto f_simplex : stree_from_alpha_complex.complex_simplex_range()) {
+    Simplex_handle sh = stree_from_delaunay_complex.find(stree_from_alpha_complex.simplex_vertex_range(f_simplex));
+    BOOST_CHECK(std::isnan(stree_from_delaunay_complex.filtration(sh)));
+    BOOST_CHECK(sh != stree_from_delaunay_complex.null_simplex());
+  }
+}