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+/*    This file is part of the Gudhi Library. The Gudhi library
+ *    (Geometric Understanding in Higher Dimensions) is a generic C++
+ *    library for computational topology.
+ *
+ *    Author(s):       Clément Maria, Pawel Dlotko, Vincent Rouvreau
+ *
+ *    Copyright (C) 2016  INRIA
+ *
+ *    This program is free software: you can redistribute it and/or modify
+ *    it under the terms of the GNU General Public License as published by
+ *    the Free Software Foundation, either version 3 of the License, or
+ *    (at your option) any later version.
+ *
+ *    This program is distributed in the hope that it will be useful,
+ *    but WITHOUT ANY WARRANTY; without even the implied warranty of
+ *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+ *    GNU General Public License for more details.
+ *
+ *    You should have received a copy of the GNU General Public License
+ *    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+ */
+
+#ifndef DOC_GRAPH_INDUCED_COMPLEX_INTRO_GRAPH_INDUCED_COMPLEX_H_
+#define DOC_GRAPH_INDUCED_COMPLEX_INTRO_GRAPH_INDUCED_COMPLEX_H_
+
+namespace Gudhi {
+
+namespace graph_induced_complex {
+
+/**  \defgroup graph_induced_complex Graph induced complex
+ * 
+ * \author    Mathieu Carrière
+ * 
+ * @{
+ * 
+ * \section complexes Graph induced complexes (GIC) and Nerves
+ * 
+ * GIC and Nerves are simplicial complexes built on top of a point cloud P.
+ *
+ * \subsection nervedefinition Nerve definition
+ *
+ * Assume you are given a cover C of your point cloud P, that is a set of subsets of P
+ * whose union is P itself. Then, the Nerve of this cover
+ * is the simplicial complex that has one k-simplex per k-fold intersection of cover elements.
+ * See also <a target="_blank" href="https://en.wikipedia.org/wiki/Nerve_of_a_covering"> Wikipedia </a>.
+ *
+ * \subsection nerveexample Example
+ *
+ * This example builds the Nerve of a point cloud sampled on a 3D human shape.
+ * The cover C comes from the preimages of intervals covering the height function.
+ * All intervals have the resolution (either the length or the number of the intervals)
+ * and gain (overlap percentage).
+ *
+ * \include
+ *
+ * When launching:
+ *
+ * \code $>
+ * \endcode
+ *
+ * the program output is:
+ *
+ * \include
+ *
+ * \section gicdefinition GIC definition
+ *
+ * Again, assume you are given a cover C of your point cloud P. Moreover, assume
+ * you are also given a graph G built on top of P. Then, for any clique in G
+ * whose nodes all belong to different elements of C, the GIC includes a corresponding
+ * simplex, whose dimension is the number of nodes in the clique minus one.
+ *
+ * \subsection gicexample Example
+ *
+ * This example builds the GIC of a point cloud sampled on a 3D human shape.
+ * The cover C comes from the preimages of intervals covering the height function,
+ * and the graph G comes from a Rips complex built with a threshold parameter.
+ * Note that if the gain is too big, the number of cliques increases a lot,
+ * which make the computation time much larger.
+ *
+ * \include
+ *
+ * When launching:
+ *
+ * \code $>
+ * \endcode
+ *
+ * the program output is:
+ *
+ * \include
+ *
+ * \subsection mapperdeltadefinition Mapper Delta
+ *
+ * If one restricts to the cliques in G whose nodes all belong to preimages of consecutive
+ * intervals (assuming the cover of the height function is minimal, i.e. no more than
+ * two intervals can intersect at a time), the GIC is of dimension one, i.e. a graph.
+ * We call this graph the Mapper Delta, since it is related to the usual Mapper (see
+ * <a target="_blank" href="https://arxiv.org/abs/1511.05823"> this article </a>).
+ *
+ * \subsection mapperdeltaexample Example
+ *
+ * Mapper Delta comes with optimal selection for the Rips threshold,
+ * the resolution and the gain of the function cover. In this example,
+ * we compute the Mapper Delta of a point cloud sampled on a 3D human shape,
+ * where the graph G comes from a Rips complex with optimal threshold,
+ * and the cover C comes from the preimages of intervals covering the height function,
+ * with optimal resolution and gain. Note that optimal threshold, resolution and gain
+ * also exist for the Nerve of this cover.
+ *
+ * \include
+ *
+ * When launching:
+ *
+ * \code $>
+ * \endcode
+ *
+ * the program output is:
+ *
+ * \include
+ *
+ * 
+ * \copyright GNU General Public License v3.                         
+ * \verbatim  Contact: gudhi-users@lists.gforge.inria.fr \endverbatim
+ */
+/** @} */  // end defgroup graph_induced_complex
+
+}  // namespace graph_induced_complex
+
+}  // namespace Gudhi
+
+#endif  // DOC_GRAPH_INDUCED_COMPLEX_INTRO_GRAPH_INDUCED_COMPLEX_H_