LEMON/LEMON-main Changeset - r586:7c12061bd271

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Changeset - r586:7c12061bd271

« 583:99a31b

587:114920 »

r586:7c12061bd271

Wed, 15 Apr 2009 04:26:13

[Not Reviewed]

0 comments (0 inline)

kpeter (Peter Kovacs)
kpeter@inf.elte.hu

Add images + fixes in the doc of connectivity tools (#262)

0 5 6

default

11 files changed with 1416 insertions and 33 deletions:

doc/images/bipartite_matching.eps

586

doc/images/bipartite_partitions.eps

113

doc/images/connected_components.eps

158

doc/images/edge_biconnected_components.eps

158

doc/images/node_biconnected_components.eps

158

doc/images/strongly_connected_components.eps

179

doc/CMakeLists.txt

doc/Makefile.am

doc/groups.dox

lemon/connectivity.h

lemon/euler.h

↑ Collapse diff ↑

doc/images/bipartite_matching.eps

Show inline comments

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doc/images/connected_components.eps

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doc/images/edge_biconnected_components.eps

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doc/images/node_biconnected_components.eps

Show inline comments

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doc/images/strongly_connected_components.eps

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doc/CMakeLists.txt

Show inline comments

 		SET(PACKAGE_NAME ${PROJECT_NAME})
 		SET(PACKAGE_VERSION ${PROJECT_VERSION})
 		SET(abs_top_srcdir ${PROJECT_SOURCE_DIR})
 		SET(abs_top_builddir ${PROJECT_BINARY_DIR})
 		CONFIGURE_FILE(
 		  ${PROJECT_SOURCE_DIR}/doc/Doxyfile.in
 		  ${PROJECT_BINARY_DIR}/doc/Doxyfile
 		  @ONLY)
 		IF(DOXYGEN_EXECUTABLE AND GHOSTSCRIPT_EXECUTABLE)
 		  FILE(MAKE_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/)
 		  IF(UNIX)
 		    ADD_CUSTOM_TARGET(html
 		      COMMAND rm -rf gen-images
 		      COMMAND mkdir gen-images
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/bipartite_matching.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_matching.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/bipartite_partitions.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_partitions.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/connected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/edge_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/edge_biconnected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/grid_graph.png ${CMAKE_CURRENT_SOURCE_DIR}/images/grid_graph.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/node_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/node_biconnected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_0.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_0.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_1.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_1.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_2.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_2.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_3.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_3.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_4.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_4.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/strongly_connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/strongly_connected_components.eps
 		      COMMAND rm -rf html
 		      COMMAND ${DOXYGEN_EXECUTABLE} Doxyfile
 		      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR})
 		  ELSEIF(WIN32)
 		    ADD_CUSTOM_TARGET(html
 		      COMMAND if exist gen-images rmdir /s /q gen-images
 		      COMMAND mkdir gen-images
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/bipartite_matching.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_matching.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/bipartite_partitions.png ${CMAKE_CURRENT_SOURCE_DIR}/images/bipartite_partitions.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/connected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/edge_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/edge_biconnected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/grid_graph.png ${CMAKE_CURRENT_SOURCE_DIR}/images/grid_graph.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/node_biconnected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/node_biconnected_components.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_0.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_0.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_1.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_1.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_2.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_2.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_3.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_3.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/nodeshape_4.png ${CMAKE_CURRENT_SOURCE_DIR}/images/nodeshape_4.eps
 		      COMMAND ${GHOSTSCRIPT_EXECUTABLE} -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4 -sDEVICE=pngalpha -r18 -sOutputFile=gen-images/strongly_connected_components.png ${CMAKE_CURRENT_SOURCE_DIR}/images/strongly_connected_components.eps
 		      COMMAND if exist html rmdir /s /q html
 		      COMMAND ${DOXYGEN_EXECUTABLE} Doxyfile
 		      WORKING_DIRECTORY ${CMAKE_CURRENT_BINARY_DIR})
 		  ENDIF(UNIX)
 		  INSTALL(
 		    DIRECTORY ${CMAKE_CURRENT_BINARY_DIR}/html/
 		    DESTINATION share/doc
 		    COMPONENT html_documentation)
 		ENDIF(DOXYGEN_EXECUTABLE AND GHOSTSCRIPT_EXECUTABLE)

doc/Makefile.am

Show inline comments

 		EXTRA_DIST += \
 			doc/Doxyfile.in \
 			doc/DoxygenLayout.xml \
 			doc/coding_style.dox \
 			doc/dirs.dox \
 			doc/groups.dox \
 			doc/lgf.dox \
 			doc/license.dox \
 			doc/mainpage.dox \
 			doc/migration.dox \
 			doc/named-param.dox \
 			doc/namespaces.dox \
 			doc/html \
 			doc/CMakeLists.txt
 		DOC_EPS_IMAGES18 = \
 			bipartite_matching.eps \
 			bipartite_partitions.eps \
 			connected_components.eps \
 			edge_biconnected_components.eps \
 			grid_graph.eps \
 			node_biconnected_components.eps \
 			nodeshape_0.eps \
 			nodeshape_1.eps \
 			nodeshape_2.eps \
 			nodeshape_3.eps \
 			nodeshape_4.eps
+			nodeshape_4.eps \
 			strongly_connected_components.eps
 		DOC_EPS_IMAGES = \
 			$(DOC_EPS_IMAGES18)
 		DOC_PNG_IMAGES = \
 			$(DOC_EPS_IMAGES:%.eps=doc/gen-images/%.png)
 		EXTRA_DIST += $(DOC_EPS_IMAGES:%=doc/images/%)
 		doc/html:
 			$(MAKE) $(AM_MAKEFLAGS) html
 		GS_COMMAND=gs -dNOPAUSE -dBATCH -q -dEPSCrop -dTextAlphaBits=4 -dGraphicsAlphaBits=4
 		$(DOC_EPS_IMAGES18:%.eps=doc/gen-images/%.png): doc/gen-images/%.png: doc/images/%.eps
 			-mkdir doc/gen-images
 			if test ${gs_found} = yes; then \
 			  $(GS_COMMAND) -sDEVICE=pngalpha -r18 -sOutputFile=$@ $<; \
 			else \
 			  echo; \
 			  echo "Ghostscript not found."; \
 			  echo; \
 			  exit 1; \
 			fi
 		html-local: $(DOC_PNG_IMAGES)
 			if test ${doxygen_found} = yes; then \
 			  cd doc; \
 			  doxygen Doxyfile; \
 			  cd ..; \
 			else \
 			  echo; \
 			  echo "Doxygen not found."; \
 			  echo; \
 			  exit 1; \
 			fi
 		clean-local:
 			-rm -rf doc/html
 			-rm -f doc/doxygen.log
 			-rm -f $(DOC_PNG_IMAGES)
 			-rm -rf doc/gen-images
 		update-external-tags:
 			wget -O doc/libstdc++.tag.tmp http://gcc.gnu.org/onlinedocs/libstdc++/latest-doxygen/libstdc++.tag && \
 			mv doc/libstdc++.tag.tmp doc/libstdc++.tag || \
 			rm doc/libstdc++.tag.tmp

doc/groups.dox

Show inline comments

@@ -362,97 +362,97 @@
 		the following optimization problem.
 		\f[ \min\sum_{a\in A} f(a) cost(a) \f]
 		\f[ \sum_{a\in\delta_{out}(v)} f(a) - \sum_{a\in\delta_{in}(v)} f(a) =
 		    supply(v) \qquad \forall v\in V \f]
 		\f[ lower(a) \leq f(a) \leq upper(a) \qquad \forall a\in A \f]
 		LEMON contains several algorithms for solving minimum cost flow problems:
 		 - \ref CycleCanceling Cycle-canceling algorithms.
 		 - \ref CapacityScaling Successive shortest path algorithm with optional
 		   capacity scaling.
 		 - \ref CostScaling Push-relabel and augment-relabel algorithms based on
 		   cost scaling.
 		 - \ref NetworkSimplex Primal network simplex algorithm with various
 		   pivot strategies.
 		*/
 		/**
 		@defgroup min_cut Minimum Cut Algorithms
 		@ingroup algs
 		\brief Algorithms for finding minimum cut in graphs.
 		This group contains the algorithms for finding minimum cut in graphs.
 		The \e minimum \e cut \e problem is to find a non-empty and non-complete
 		\f$X\f$ subset of the nodes with minimum overall capacity on
 		outgoing arcs. Formally, there is a \f$G=(V,A)\f$ digraph, a
 		\f$cap: A\rightarrow\mathbf{R}^+_0\f$ capacity function. The minimum
 		cut is the \f$X\f$ solution of the next optimization problem:
 		\f[ \min_{X \subset V, X\not\in \{\emptyset, V\}}
 		    \sum_{uv\in A, u\in X, v\not\in X}cap(uv) \f]
 		LEMON contains several algorithms related to minimum cut problems:
 		- \ref HaoOrlin "Hao-Orlin algorithm" for calculating minimum cut
 		  in directed graphs.
 		- \ref NagamochiIbaraki "Nagamochi-Ibaraki algorithm" for
 		  calculating minimum cut in undirected graphs.
 		- \ref GomoryHu "Gomory-Hu tree computation" for calculating
 		  all-pairs minimum cut in undirected graphs.
 		If you want to find minimum cut just between two distinict nodes,
 		see the \ref max_flow "maximum flow problem".
 		*/
 		/**
-		@defgroup graph_prop Connectivity and Other Graph Properties
+		@defgroup graph_properties Connectivity and Other Graph Properties
 		@ingroup algs
 		\brief Algorithms for discovering the graph properties
 		This group contains the algorithms for discovering the graph properties
 		like connectivity, bipartiteness, euler property, simplicity etc.
 		\image html edge_biconnected_components.png
 		\image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
 		*/
 		/**
 		@defgroup planar Planarity Embedding and Drawing
 		@ingroup algs
 		\brief Algorithms for planarity checking, embedding and drawing
 		This group contains the algorithms for planarity checking,
 		embedding and drawing.
 		\image html planar.png
 		\image latex planar.eps "Plane graph" width=\textwidth
 		*/
 		/**
 		@defgroup matching Matching Algorithms
 		@ingroup algs
 		\brief Algorithms for finding matchings in graphs and bipartite graphs.
 		This group contains algorithm objects and functions to calculate
 		matchings in graphs and bipartite graphs. The general matching problem is
 		finding a subset of the arcs which does not shares common endpoints.
 		There are several different algorithms for calculate matchings in
 		graphs.  The matching problems in bipartite graphs are generally
 		easier than in general graphs. The goal of the matching optimization
 		can be finding maximum cardinality, maximum weight or minimum cost
 		matching. The search can be constrained to find perfect or
 		maximum cardinality matching.
 		The matching algorithms implemented in LEMON:
 		- \ref MaxBipartiteMatching Hopcroft-Karp augmenting path algorithm
 		  for calculating maximum cardinality matching in bipartite graphs.
 		- \ref PrBipartiteMatching Push-relabel algorithm
 		  for calculating maximum cardinality matching in bipartite graphs.
 		- \ref MaxWeightedBipartiteMatching
 		  Successive shortest path algorithm for calculating maximum weighted
 		  matching and maximum weighted bipartite matching in bipartite graphs.
 		- \ref MinCostMaxBipartiteMatching
 		  Successive shortest path algorithm for calculating minimum cost maximum

lemon/connectivity.h

Show inline comments

 		/* -*- mode: C++; indent-tabs-mode: nil; -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library.
+		 *
 		 * Copyright (C) 2003-2009
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_CONNECTIVITY_H
 		#define LEMON_CONNECTIVITY_H
 		#include <lemon/dfs.h>
 		#include <lemon/bfs.h>
 		#include <lemon/core.h>
 		#include <lemon/maps.h>
 		#include <lemon/adaptors.h>
 		#include <lemon/concepts/digraph.h>
 		#include <lemon/concepts/graph.h>
 		#include <lemon/concept_check.h>
 		#include <stack>
 		#include <functional>
-		/// \ingroup connectivity
+		/// \ingroup graph_properties
 		/// \file
 		/// \brief Connectivity algorithms
 		///
 		/// Connectivity algorithms
 		namespace lemon {
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check whether the given undirected graph is connected.
 		  ///
 		  /// Check whether the given undirected graph is connected.
 		  /// \param graph The undirected graph.
 		  /// \return \c true when there is path between any two nodes in the graph.
 		  /// \note By definition, the empty graph is connected.
 		  template <typename Graph>
 		  bool connected(const Graph& graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    if (NodeIt(graph) == INVALID) return true;
 		    Dfs<Graph> dfs(graph);
 		    dfs.run(NodeIt(graph));
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        return false;
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Count the number of connected components of an undirected graph
 		  ///
 		  /// Count the number of connected components of an undirected graph
 		  ///
 		  /// \param graph The graph. It must be undirected.
 		  /// \return The number of components
 		  /// \note By definition, the empty graph consists
 		  /// of zero connected components.
 		  template <typename Graph>
 		  int countConnectedComponents(const Graph &graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::Arc Arc;
 		    typedef NullMap<Node, Arc> PredMap;
 		    typedef NullMap<Node, int> DistMap;
 		    int compNum = 0;
 		    typename Bfs<Graph>::
 		      template SetPredMap<PredMap>::
 		      template SetDistMap<DistMap>::
 		      Create bfs(graph);
 		    PredMap predMap;
 		    bfs.predMap(predMap);
 		    DistMap distMap;
 		    bfs.distMap(distMap);
 		    bfs.init();
 		    for(typename Graph::NodeIt n(graph); n != INVALID; ++n) {
 		      if (!bfs.reached(n)) {
 		        bfs.addSource(n);
 		        bfs.start();
 		        ++compNum;
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the connected components of an undirected graph
 		  ///
 		  /// Find the connected components of an undirected graph.
 		  ///
 		  /// \image html connected_components.png
 		  /// \image latex connected_components.eps "Connected components" width=\textwidth
 		  ///
 		  /// \param graph The graph. It must be undirected.
 		  /// \retval compMap A writable node map. The values will be set from 0 to
 		  /// the number of the connected components minus one. Each values of the map
 		  /// will be set exactly once, the values of a certain component will be
 		  /// set continuously.
 		  /// \return The number of components
 		  ///
 		  template <class Graph, class NodeMap>
 		  int connectedComponents(const Graph &graph, NodeMap &compMap) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::Arc Arc;
 		    checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
 		    typedef NullMap<Node, Arc> PredMap;
 		    typedef NullMap<Node, int> DistMap;
 		    int compNum = 0;
 		    typename Bfs<Graph>::
 		      template SetPredMap<PredMap>::
 		      template SetDistMap<DistMap>::
 		      Create bfs(graph);
 		    PredMap predMap;
 		    bfs.predMap(predMap);
 		    DistMap distMap;
 		    bfs.distMap(distMap);
 		    bfs.init();
 		    for(typename Graph::NodeIt n(graph); n != INVALID; ++n) {
 		      if(!bfs.reached(n)) {
 		        bfs.addSource(n);
 		        while (!bfs.emptyQueue()) {
 		          compMap.set(bfs.nextNode(), compNum);
 		          bfs.processNextNode();
+		        }
 		        ++compNum;
+		      }
+		    }
 		    return compNum;
+		  }
 		  namespace _connectivity_bits {
 		    template <typename Digraph, typename Iterator >
 		    struct LeaveOrderVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      LeaveOrderVisitor(Iterator it) : _it(it) {}
 		      void leave(const Node& node) {
 		        *(_it++) = node;
+		      }
@@ -182,286 +184,288 @@
 		      void reach(const Node& node) {
 		        _map.set(node, _value);
+		      }
 		    private:
 		      Map& _map;
 		      Value& _value;
 		    };
 		    template <typename Digraph, typename ArcMap>
 		    struct StronglyConnectedCutArcsVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      StronglyConnectedCutArcsVisitor(const Digraph& digraph,
 		                                      ArcMap& cutMap,
 		                                      int& cutNum)
 		        : _digraph(digraph), _cutMap(cutMap), _cutNum(cutNum),
 		          _compMap(digraph, -1), _num(-1) {
+		      }
 		      void start(const Node&) {
 		        ++_num;
+		      }
 		      void reach(const Node& node) {
 		        _compMap.set(node, _num);
+		      }
 		      void examine(const Arc& arc) {
 		         if (_compMap[_digraph.source(arc)] !=
 		             _compMap[_digraph.target(arc)]) {
 		           _cutMap.set(arc, true);
 		           ++_cutNum;
+		         }
+		      }
 		    private:
 		      const Digraph& _digraph;
 		      ArcMap& _cutMap;
 		      int& _cutNum;
 		      typename Digraph::template NodeMap<int> _compMap;
 		      int _num;
 		    };
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check whether the given directed graph is strongly connected.
 		  ///
 		  /// Check whether the given directed graph is strongly connected. The
 		  /// graph is strongly connected when any two nodes of the graph are
 		  /// connected with directed paths in both direction.
 		  /// \return \c false when the graph is not strongly connected.
 		  /// \see connected
 		  ///
 		  /// \note By definition, the empty graph is strongly connected.
 		  template <typename Digraph>
 		  bool stronglyConnected(const Digraph& digraph) {
 		    checkConcept<concepts::Digraph, Digraph>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typename Digraph::Node source = NodeIt(digraph);
 		    if (source == INVALID) return true;
 		    using namespace _connectivity_bits;
 		    typedef DfsVisitor<Digraph> Visitor;
 		    Visitor visitor;
 		    DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
 		    dfs.init();
 		    dfs.addSource(source);
 		    dfs.start();
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        return false;
+		      }
+		    }
 		    typedef ReverseDigraph<const Digraph> RDigraph;
 		    typedef typename RDigraph::NodeIt RNodeIt;
 		    RDigraph rdigraph(digraph);
 		    typedef DfsVisitor<Digraph> RVisitor;
 		    RVisitor rvisitor;
 		    DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
 		    rdfs.init();
 		    rdfs.addSource(source);
 		    rdfs.start();
 		    for (RNodeIt it(rdigraph); it != INVALID; ++it) {
 		      if (!rdfs.reached(it)) {
 		        return false;
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Count the strongly connected components of a directed graph
 		  ///
 		  /// Count the strongly connected components of a directed graph.
 		  /// The strongly connected components are the classes of an
 		  /// equivalence relation on the nodes of the graph. Two nodes are in
 		  /// the same class if they are connected with directed paths in both
 		  /// direction.
 		  ///
 		  /// \param digraph The graph.
 		  /// \return The number of components
 		  /// \note By definition, the empty graph has zero
 		  /// strongly connected components.
 		  template <typename Digraph>
 		  int countStronglyConnectedComponents(const Digraph& digraph) {
 		    checkConcept<concepts::Digraph, Digraph>();
 		    using namespace _connectivity_bits;
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::ArcIt ArcIt;
 		    typedef std::vector<Node> Container;
 		    typedef typename Container::iterator Iterator;
 		    Container nodes(countNodes(digraph));
 		    typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
 		    Visitor visitor(nodes.begin());
 		    DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
 		    dfs.init();
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    typedef typename Container::reverse_iterator RIterator;
 		    typedef ReverseDigraph<const Digraph> RDigraph;
 		    RDigraph rdigraph(digraph);
 		    typedef DfsVisitor<Digraph> RVisitor;
 		    RVisitor rvisitor;
 		    DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
 		    int compNum = 0;
 		    rdfs.init();
 		    for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
 		      if (!rdfs.reached(*it)) {
 		        rdfs.addSource(*it);
 		        rdfs.start();
 		        ++compNum;
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the strongly connected components of a directed graph
 		  ///
 		  /// Find the strongly connected components of a directed graph.  The
 		  /// strongly connected components are the classes of an equivalence
 		  /// relation on the nodes of the graph. Two nodes are in
 		  /// relationship when there are directed paths between them in both
 		  /// direction. In addition, the numbering of components will satisfy
 		  /// that there is no arc going from a higher numbered component to
 		  /// a lower.
 		  ///
 		  /// \image html strongly_connected_components.png
 		  /// \image latex strongly_connected_components.eps "Strongly connected components" width=\textwidth
 		  ///
 		  /// \param digraph The digraph.
 		  /// \retval compMap A writable node map. The values will be set from 0 to
 		  /// the number of the strongly connected components minus one. Each value
 		  /// of the map will be set exactly once, the values of a certain component
 		  /// will be set continuously.
 		  /// \return The number of components
 		  ///
 		  template <typename Digraph, typename NodeMap>
 		  int stronglyConnectedComponents(const Digraph& digraph, NodeMap& compMap) {
 		    checkConcept<concepts::Digraph, Digraph>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
 		    using namespace _connectivity_bits;
 		    typedef std::vector<Node> Container;
 		    typedef typename Container::iterator Iterator;
 		    Container nodes(countNodes(digraph));
 		    typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
 		    Visitor visitor(nodes.begin());
 		    DfsVisit<Digraph, Visitor> dfs(digraph, visitor);
 		    dfs.init();
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    typedef typename Container::reverse_iterator RIterator;
 		    typedef ReverseDigraph<const Digraph> RDigraph;
 		    RDigraph rdigraph(digraph);
 		    int compNum = 0;
 		    typedef FillMapVisitor<RDigraph, NodeMap> RVisitor;
 		    RVisitor rvisitor(compMap, compNum);
 		    DfsVisit<RDigraph, RVisitor> rdfs(rdigraph, rvisitor);
 		    rdfs.init();
 		    for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
 		      if (!rdfs.reached(*it)) {
 		        rdfs.addSource(*it);
 		        rdfs.start();
 		        ++compNum;
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the cut arcs of the strongly connected components.
 		  ///
 		  /// Find the cut arcs of the strongly connected components.
 		  /// The strongly connected components are the classes of an equivalence
 		  /// relation on the nodes of the graph. Two nodes are in relationship
 		  /// when there are directed paths between them in both direction.
 		  /// The strongly connected components are separated by the cut arcs.
 		  ///
 		  /// \param graph The graph.
 		  /// \retval cutMap A writable node map. The values will be set true when the
 		  /// arc is a cut arc.
 		  ///
 		  /// \return The number of cut arcs
 		  template <typename Digraph, typename ArcMap>
 		  int stronglyConnectedCutArcs(const Digraph& graph, ArcMap& cutMap) {
 		    checkConcept<concepts::Digraph, Digraph>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    checkConcept<concepts::WriteMap<Arc, bool>, ArcMap>();
 		    using namespace _connectivity_bits;
 		    typedef std::vector<Node> Container;
 		    typedef typename Container::iterator Iterator;
 		    Container nodes(countNodes(graph));
 		    typedef LeaveOrderVisitor<Digraph, Iterator> Visitor;
 		    Visitor visitor(nodes.begin());
 		    DfsVisit<Digraph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    typedef typename Container::reverse_iterator RIterator;
 		    typedef ReverseDigraph<const Digraph> RDigraph;
 		    RDigraph rgraph(graph);
 		    int cutNum = 0;
 		    typedef StronglyConnectedCutArcsVisitor<RDigraph, ArcMap> RVisitor;
@@ -655,190 +659,192 @@
+		          }
 		          return;
+		        }
 		        if (_predMap[_graph.source(edge)] == _graph.target(edge)) return;
 		        if (_retMap[_graph.source(edge)] > _numMap[_graph.target(edge)]) {
 		          _retMap.set(_graph.source(edge), _numMap[_graph.target(edge)]);
+		        }
+		      }
 		      void backtrack(const Arc& edge) {
 		        if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
 		          _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
+		        }
 		        if (_numMap[_graph.source(edge)] <= _retMap[_graph.target(edge)]) {
 		          if (_predMap[_graph.source(edge)] != INVALID) {
 		            if (!_cutMap[_graph.source(edge)]) {
 		              _cutMap.set(_graph.source(edge), true);
 		              ++_cutNum;
+		            }
 		          } else if (rootCut) {
 		            if (!_cutMap[_graph.source(edge)]) {
 		              _cutMap.set(_graph.source(edge), true);
 		              ++_cutNum;
+		            }
 		          } else {
 		            rootCut = true;
+		          }
+		        }
+		      }
 		    private:
 		      const Digraph& _graph;
 		      NodeMap& _cutMap;
 		      int& _cutNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Node> _predMap;
 		      std::stack<Edge> _edgeStack;
 		      int _num;
 		      bool rootCut;
 		    };
+		  }
 		  template <typename Graph>
 		  int countBiNodeConnectedComponents(const Graph& graph);
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Checks the graph is bi-node-connected.
 		  ///
 		  /// This function checks that the undirected graph is bi-node-connected
 		  /// graph. The graph is bi-node-connected if any two undirected edge is
 		  /// on same circle.
 		  ///
 		  /// \param graph The graph.
 		  /// \return \c true when the graph bi-node-connected.
 		  template <typename Graph>
 		  bool biNodeConnected(const Graph& graph) {
 		    return countBiNodeConnectedComponents(graph) <= 1;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Count the biconnected components.
 		  ///
 		  /// This function finds the bi-node-connected components in an undirected
 		  /// graph. The biconnected components are the classes of an equivalence
 		  /// relation on the undirected edges. Two undirected edge is in relationship
 		  /// when they are on same circle.
 		  ///
 		  /// \param graph The graph.
 		  /// \return The number of components.
 		  template <typename Graph>
 		  int countBiNodeConnectedComponents(const Graph& graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    using namespace _connectivity_bits;
 		    typedef CountBiNodeConnectedComponentsVisitor<Graph> Visitor;
 		    int compNum = 0;
 		    Visitor visitor(graph, compNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the bi-node-connected components.
 		  ///
 		  /// This function finds the bi-node-connected components in an undirected
 		  /// graph. The bi-node-connected components are the classes of an equivalence
 		  /// relation on the undirected edges. Two undirected edge are in relationship
 		  /// when they are on same circle.
 		  ///
 		  /// \image html node_biconnected_components.png
 		  /// \image latex node_biconnected_components.eps "bi-node-connected components" width=\textwidth
 		  ///
 		  /// \param graph The graph.
 		  /// \retval compMap A writable uedge map. The values will be set from 0
 		  /// to the number of the biconnected components minus one. Each values
 		  /// of the map will be set exactly once, the values of a certain component
 		  /// will be set continuously.
 		  /// \return The number of components.
 		  ///
 		  template <typename Graph, typename EdgeMap>
 		  int biNodeConnectedComponents(const Graph& graph,
 		                                EdgeMap& compMap) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::Edge Edge;
 		    checkConcept<concepts::WriteMap<Edge, int>, EdgeMap>();
 		    using namespace _connectivity_bits;
 		    typedef BiNodeConnectedComponentsVisitor<Graph, EdgeMap> Visitor;
 		    int compNum = 0;
 		    Visitor visitor(graph, compMap, compNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the bi-node-connected cut nodes.
 		  ///
 		  /// This function finds the bi-node-connected cut nodes in an undirected
 		  /// graph. The bi-node-connected components are the classes of an equivalence
 		  /// relation on the undirected edges. Two undirected edges are in
 		  /// relationship when they are on same circle. The biconnected components
 		  /// are separted by nodes which are the cut nodes of the components.
 		  ///
 		  /// \param graph The graph.
 		  /// \retval cutMap A writable edge map. The values will be set true when
 		  /// the node separate two or more components.
 		  /// \return The number of the cut nodes.
 		  template <typename Graph, typename NodeMap>
 		  int biNodeConnectedCutNodes(const Graph& graph, NodeMap& cutMap) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::NodeIt NodeIt;
 		    checkConcept<concepts::WriteMap<Node, bool>, NodeMap>();
 		    using namespace _connectivity_bits;
 		    typedef BiNodeConnectedCutNodesVisitor<Graph, NodeMap> Visitor;
 		    int cutNum = 0;
 		    Visitor visitor(graph, cutMap, cutNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return cutNum;
+		  }
 		  namespace _connectivity_bits {
 		    template <typename Digraph>
 		    class CountBiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
@@ -978,559 +984,565 @@
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        ++_num;
+		      }
 		      void leave(const Node& node) {
 		        if (_numMap[node] <= _retMap[node]) {
 		          if (_predMap[node] != INVALID) {
 		            _cutMap.set(_predMap[node], true);
 		            ++_cutNum;
+		          }
+		        }
+		      }
 		      void discover(const Arc& edge) {
 		        _predMap.set(_graph.target(edge), edge);
+		      }
 		      void examine(const Arc& edge) {
 		        if (_predMap[_graph.source(edge)] == _graph.oppositeArc(edge)) {
 		          return;
+		        }
 		        if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
 		          _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
+		        }
+		      }
 		      void backtrack(const Arc& edge) {
 		        if (_retMap[_graph.source(edge)] > _retMap[_graph.target(edge)]) {
 		          _retMap.set(_graph.source(edge), _retMap[_graph.target(edge)]);
+		        }
+		      }
 		    private:
 		      const Digraph& _graph;
 		      ArcMap& _cutMap;
 		      int& _cutNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Arc> _predMap;
 		      int _num;
 		    };
+		  }
 		  template <typename Graph>
 		  int countBiEdgeConnectedComponents(const Graph& graph);
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Checks that the graph is bi-edge-connected.
 		  ///
 		  /// This function checks that the graph is bi-edge-connected. The undirected
 		  /// graph is bi-edge-connected when any two nodes are connected with two
 		  /// edge-disjoint paths.
 		  ///
 		  /// \param graph The undirected graph.
 		  /// \return The number of components.
 		  template <typename Graph>
 		  bool biEdgeConnected(const Graph& graph) {
 		    return countBiEdgeConnectedComponents(graph) <= 1;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Count the bi-edge-connected components.
 		  ///
 		  /// This function count the bi-edge-connected components in an undirected
 		  /// graph. The bi-edge-connected components are the classes of an equivalence
 		  /// relation on the nodes. Two nodes are in relationship when they are
 		  /// connected with at least two edge-disjoint paths.
 		  ///
 		  /// \param graph The undirected graph.
 		  /// \return The number of components.
 		  template <typename Graph>
 		  int countBiEdgeConnectedComponents(const Graph& graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    using namespace _connectivity_bits;
 		    typedef CountBiEdgeConnectedComponentsVisitor<Graph> Visitor;
 		    int compNum = 0;
 		    Visitor visitor(graph, compNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the bi-edge-connected components.
 		  ///
 		  /// This function finds the bi-edge-connected components in an undirected
 		  /// graph. The bi-edge-connected components are the classes of an equivalence
 		  /// relation on the nodes. Two nodes are in relationship when they are
 		  /// connected at least two edge-disjoint paths.
 		  ///
 		  /// \image html edge_biconnected_components.png
 		  /// \image latex edge_biconnected_components.eps "bi-edge-connected components" width=\textwidth
 		  ///
 		  /// \param graph The graph.
 		  /// \retval compMap A writable node map. The values will be set from 0 to
 		  /// the number of the biconnected components minus one. Each values
 		  /// of the map will be set exactly once, the values of a certain component
 		  /// will be set continuously.
 		  /// \return The number of components.
 		  ///
 		  template <typename Graph, typename NodeMap>
 		  int biEdgeConnectedComponents(const Graph& graph, NodeMap& compMap) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::Node Node;
 		    checkConcept<concepts::WriteMap<Node, int>, NodeMap>();
 		    using namespace _connectivity_bits;
 		    typedef BiEdgeConnectedComponentsVisitor<Graph, NodeMap> Visitor;
 		    int compNum = 0;
 		    Visitor visitor(graph, compMap, compNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return compNum;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Find the bi-edge-connected cut edges.
 		  ///
 		  /// This function finds the bi-edge-connected components in an undirected
 		  /// graph. The bi-edge-connected components are the classes of an equivalence
 		  /// relation on the nodes. Two nodes are in relationship when they are
 		  /// connected with at least two edge-disjoint paths. The bi-edge-connected
 		  /// components are separted by edges which are the cut edges of the
 		  /// components.
 		  ///
 		  /// \param graph The graph.
 		  /// \retval cutMap A writable node map. The values will be set true when the
 		  /// edge is a cut edge.
 		  /// \return The number of cut edges.
 		  template <typename Graph, typename EdgeMap>
 		  int biEdgeConnectedCutEdges(const Graph& graph, EdgeMap& cutMap) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::Edge Edge;
 		    checkConcept<concepts::WriteMap<Edge, bool>, EdgeMap>();
 		    using namespace _connectivity_bits;
 		    typedef BiEdgeConnectedCutEdgesVisitor<Graph, EdgeMap> Visitor;
 		    int cutNum = 0;
 		    Visitor visitor(graph, cutMap, cutNum);
 		    DfsVisit<Graph, Visitor> dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
 		    return cutNum;
+		  }
 		  namespace _connectivity_bits {
 		    template <typename Digraph, typename IntNodeMap>
 		    class TopologicalSortVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc edge;
 		      TopologicalSortVisitor(IntNodeMap& order, int num)
 		        : _order(order), _num(num) {}
 		      void leave(const Node& node) {
 		        _order.set(node, --_num);
+		      }
 		    private:
 		      IntNodeMap& _order;
 		      int _num;
 		    };
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Sort the nodes of a DAG into topolgical order.
 		  ///
 		  /// Sort the nodes of a DAG into topolgical order.
 		  ///
 		  /// \param graph The graph. It must be directed and acyclic.
 		  /// \retval order A writable node map. The values will be set from 0 to
 		  /// the number of the nodes in the graph minus one. Each values of the map
 		  /// will be set exactly once, the values  will be set descending order.
 		  ///
 		  /// \see checkedTopologicalSort
 		  /// \see dag
 		  template <typename Digraph, typename NodeMap>
 		  void topologicalSort(const Digraph& graph, NodeMap& order) {
 		    using namespace _connectivity_bits;
 		    checkConcept<concepts::Digraph, Digraph>();
 		    checkConcept<concepts::WriteMap<typename Digraph::Node, int>, NodeMap>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    TopologicalSortVisitor<Digraph, NodeMap>
 		      visitor(order, countNodes(graph));
 		    DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> >
 		      dfs(graph, visitor);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        dfs.start();
+		      }
+		    }
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Sort the nodes of a DAG into topolgical order.
 		  ///
 		  /// Sort the nodes of a DAG into topolgical order. It also checks
 		  /// that the given graph is DAG.
 		  ///
 		  /// \param digraph The graph. It must be directed and acyclic.
 		  /// \retval order A readable - writable node map. The values will be set
 		  /// from 0 to the number of the nodes in the graph minus one. Each values
 		  /// of the map will be set exactly once, the values will be set descending
 		  /// order.
 		  /// \return \c false when the graph is not DAG.
 		  ///
 		  /// \see topologicalSort
 		  /// \see dag
 		  template <typename Digraph, typename NodeMap>
 		  bool checkedTopologicalSort(const Digraph& digraph, NodeMap& order) {
 		    using namespace _connectivity_bits;
 		    checkConcept<concepts::Digraph, Digraph>();
 		    checkConcept<concepts::ReadWriteMap<typename Digraph::Node, int>,
 		      NodeMap>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      order.set(it, -1);
+		    }
 		    TopologicalSortVisitor<Digraph, NodeMap>
 		      visitor(order, countNodes(digraph));
 		    DfsVisit<Digraph, TopologicalSortVisitor<Digraph, NodeMap> >
 		      dfs(digraph, visitor);
 		    dfs.init();
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        while (!dfs.emptyQueue()) {
 		           Arc arc = dfs.nextArc();
 		           Node target = digraph.target(arc);
 		           if (dfs.reached(target) && order[target] == -1) {
 		             return false;
+		           }
 		           dfs.processNextArc();
+		         }
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check that the given directed graph is a DAG.
 		  ///
 		  /// Check that the given directed graph is a DAG. The DAG is
 		  /// an Directed Acyclic Digraph.
 		  /// \return \c false when the graph is not DAG.
 		  /// \see acyclic
 		  template <typename Digraph>
 		  bool dag(const Digraph& digraph) {
 		    checkConcept<concepts::Digraph, Digraph>();
 		    typedef typename Digraph::Node Node;
 		    typedef typename Digraph::NodeIt NodeIt;
 		    typedef typename Digraph::Arc Arc;
 		    typedef typename Digraph::template NodeMap<bool> ProcessedMap;
 		    typename Dfs<Digraph>::template SetProcessedMap<ProcessedMap>::
 		      Create dfs(digraph);
 		    ProcessedMap processed(digraph);
 		    dfs.processedMap(processed);
 		    dfs.init();
 		    for (NodeIt it(digraph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        while (!dfs.emptyQueue()) {
 		          Arc edge = dfs.nextArc();
 		          Node target = digraph.target(edge);
 		          if (dfs.reached(target) && !processed[target]) {
 		            return false;
+		          }
 		          dfs.processNextArc();
+		        }
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check that the given undirected graph is acyclic.
 		  ///
 		  /// Check that the given undirected graph acyclic.
 		  /// \param graph The undirected graph.
 		  /// \return \c true when there is no circle in the graph.
 		  /// \see dag
 		  template <typename Graph>
 		  bool acyclic(const Graph& graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::Arc Arc;
 		    Dfs<Graph> dfs(graph);
 		    dfs.init();
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        dfs.addSource(it);
 		        while (!dfs.emptyQueue()) {
 		          Arc edge = dfs.nextArc();
 		          Node source = graph.source(edge);
 		          Node target = graph.target(edge);
 		          if (dfs.reached(target) &&
 		              dfs.predArc(source) != graph.oppositeArc(edge)) {
 		            return false;
+		          }
 		          dfs.processNextArc();
+		        }
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check that the given undirected graph is tree.
 		  ///
 		  /// Check that the given undirected graph is tree.
 		  /// \param graph The undirected graph.
 		  /// \return \c true when the graph is acyclic and connected.
 		  template <typename Graph>
 		  bool tree(const Graph& graph) {
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::Arc Arc;
 		    Dfs<Graph> dfs(graph);
 		    dfs.init();
 		    dfs.addSource(NodeIt(graph));
 		    while (!dfs.emptyQueue()) {
 		      Arc edge = dfs.nextArc();
 		      Node source = graph.source(edge);
 		      Node target = graph.target(edge);
 		      if (dfs.reached(target) &&
 		          dfs.predArc(source) != graph.oppositeArc(edge)) {
 		        return false;
+		      }
 		      dfs.processNextArc();
+		    }
 		    for (NodeIt it(graph); it != INVALID; ++it) {
 		      if (!dfs.reached(it)) {
 		        return false;
+		      }
+		    }
 		    return true;
+		  }
 		  namespace _connectivity_bits {
 		    template <typename Digraph>
 		    class BipartiteVisitor : public BfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Node Node;
 		      BipartiteVisitor(const Digraph& graph, bool& bipartite)
 		        : _graph(graph), _part(graph), _bipartite(bipartite) {}
 		      void start(const Node& node) {
 		        _part[node] = true;
+		      }
 		      void discover(const Arc& edge) {
 		        _part.set(_graph.target(edge), !_part[_graph.source(edge)]);
+		      }
 		      void examine(const Arc& edge) {
 		        _bipartite = _bipartite &&
 		          _part[_graph.target(edge)] != _part[_graph.source(edge)];
+		      }
 		    private:
 		      const Digraph& _graph;
 		      typename Digraph::template NodeMap<bool> _part;
 		      bool& _bipartite;
 		    };
 		    template <typename Digraph, typename PartMap>
 		    class BipartitePartitionsVisitor : public BfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Node Node;
 		      BipartitePartitionsVisitor(const Digraph& graph,
 		                                 PartMap& part, bool& bipartite)
 		        : _graph(graph), _part(part), _bipartite(bipartite) {}
 		      void start(const Node& node) {
 		        _part.set(node, true);
+		      }
 		      void discover(const Arc& edge) {
 		        _part.set(_graph.target(edge), !_part[_graph.source(edge)]);
+		      }
 		      void examine(const Arc& edge) {
 		        _bipartite = _bipartite &&
 		          _part[_graph.target(edge)] != _part[_graph.source(edge)];
+		      }
 		    private:
 		      const Digraph& _graph;
 		      PartMap& _part;
 		      bool& _bipartite;
 		    };
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check if the given undirected graph is bipartite or not
 		  ///
 		  /// The function checks if the given undirected \c graph graph is bipartite
 		  /// or not. The \ref Bfs algorithm is used to calculate the result.
 		  /// \param graph The undirected graph.
 		  /// \return \c true if \c graph is bipartite, \c false otherwise.
 		  /// \sa bipartitePartitions
 		  template<typename Graph>
 		  inline bool bipartite(const Graph &graph){
 		    using namespace _connectivity_bits;
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::ArcIt ArcIt;
 		    bool bipartite = true;
 		    BipartiteVisitor<Graph>
 		      visitor(graph, bipartite);
 		    BfsVisit<Graph, BipartiteVisitor<Graph> >
 		      bfs(graph, visitor);
 		    bfs.init();
 		    for(NodeIt it(graph); it != INVALID; ++it) {
 		      if(!bfs.reached(it)){
 		        bfs.addSource(it);
 		        while (!bfs.emptyQueue()) {
 		          bfs.processNextNode();
 		          if (!bipartite) return false;
+		        }
+		      }
+		    }
 		    return true;
+		  }
-		  /// \ingroup connectivity
+		  /// \ingroup graph_properties
 		  ///
 		  /// \brief Check if the given undirected graph is bipartite or not
 		  ///
 		  /// The function checks if the given undirected graph is bipartite
 		  /// or not. The  \ref  Bfs  algorithm  is   used  to  calculate the result.
 		  /// During the execution, the \c partMap will be set as the two
 		  /// partitions of the graph.
 		  ///
 		  /// \image html bipartite_partitions.png
 		  /// \image latex bipartite_partitions.eps "Bipartite partititions" width=\textwidth
 		  ///
 		  /// \param graph The undirected graph.
 		  /// \retval partMap A writable bool map of nodes. It will be set as the
 		  /// two partitions of the graph.
 		  /// \return \c true if \c graph is bipartite, \c false otherwise.
 		  template<typename Graph, typename NodeMap>
 		  inline bool bipartitePartitions(const Graph &graph, NodeMap &partMap){
 		    using namespace _connectivity_bits;
 		    checkConcept<concepts::Graph, Graph>();
 		    typedef typename Graph::Node Node;
 		    typedef typename Graph::NodeIt NodeIt;
 		    typedef typename Graph::ArcIt ArcIt;
 		    bool bipartite = true;
 		    BipartitePartitionsVisitor<Graph, NodeMap>
 		      visitor(graph, partMap, bipartite);
 		    BfsVisit<Graph, BipartitePartitionsVisitor<Graph, NodeMap> >
 		      bfs(graph, visitor);
 		    bfs.init();
 		    for(NodeIt it(graph); it != INVALID; ++it) {
 		      if(!bfs.reached(it)){
 		        bfs.addSource(it);
 		        while (!bfs.emptyQueue()) {
 		          bfs.processNextNode();
 		          if (!bipartite) return false;
+		        }
+		      }
+		    }
 		    return true;
+		  }
 		  /// \brief Returns true when there are not loop edges in the graph.
 		  ///
 		  /// Returns true when there are not loop edges in the graph.
 		  template <typename Digraph>
 		  bool loopFree(const Digraph& digraph) {
 		    for (typename Digraph::ArcIt it(digraph); it != INVALID; ++it) {
 		      if (digraph.source(it) == digraph.target(it)) return false;
+		    }
 		    return true;
+		  }
 		  /// \brief Returns true when there are not parallel edges in the graph.
 		  ///
 		  /// Returns true when there are not parallel edges in the graph.
 		  template <typename Digraph>

lemon/euler.h

Show inline comments

 		/* -*- mode: C++; indent-tabs-mode: nil; -*-
+		 *
 		 * This file is a part of LEMON, a generic C++ optimization library.
+		 *
 		 * Copyright (C) 2003-2009
 		 * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport
 		 * (Egervary Research Group on Combinatorial Optimization, EGRES).
+		 *
 		 * Permission to use, modify and distribute this software is granted
 		 * provided that this copyright notice appears in all copies. For
 		 * precise terms see the accompanying LICENSE file.
+		 *
 		 * This software is provided "AS IS" with no warranty of any kind,
 		 * express or implied, and with no claim as to its suitability for any
 		 * purpose.
+		 *
 		 */
 		#ifndef LEMON_EULER_H
 		#define LEMON_EULER_H
 		#include<lemon/core.h>
 		#include<lemon/adaptors.h>
 		#include<lemon/connectivity.h>
 		#include <list>
-		/// \ingroup graph_prop
+		/// \ingroup graph_properties
 		/// \file
 		/// \brief Euler tour
 		///
 		///This file provides an Euler tour iterator and ways to check
 		///if a digraph is euler.
 		namespace lemon {
 		  ///Euler iterator for digraphs.
-		  /// \ingroup graph_prop
+		  /// \ingroup graph_properties
 		  ///This iterator converts to the \c Arc type of the digraph and using
 		  ///operator ++, it provides an Euler tour of a \e directed
 		  ///graph (if there exists).
 		  ///
 		  ///For example
 		  ///if the given digraph is Euler (i.e it has only one nontrivial component
 		  ///and the in-degree is equal to the out-degree for all nodes),
 		  ///the following code will put the arcs of \c g
 		  ///to the vector \c et according to an
 		  ///Euler tour of \c g.
 		  ///\code
 		  ///  std::vector<ListDigraph::Arc> et;
 		  ///  for(DiEulerIt<ListDigraph> e(g),e!=INVALID;++e)
 		  ///    et.push_back(e);
 		  ///\endcode
 		  ///If \c g is not Euler then the resulted tour will not be full or closed.
 		  ///\sa EulerIt
 		  template<typename GR>
 		  class DiEulerIt
+		  {
 		    typedef typename GR::Node Node;
 		    typedef typename GR::NodeIt NodeIt;
 		    typedef typename GR::Arc Arc;
 		    typedef typename GR::ArcIt ArcIt;
 		    typedef typename GR::OutArcIt OutArcIt;
 		    typedef typename GR::InArcIt InArcIt;
 		    const GR &g;
 		    typename GR::template NodeMap<OutArcIt> nedge;
 		    std::list<Arc> euler;
 		  public:
 		    ///Constructor
 		    ///\param gr A digraph.
 		    ///\param start The starting point of the tour. If it is not given
 		    ///       the tour will start from the first node.
 		    DiEulerIt(const GR &gr, typename GR::Node start = INVALID)
 		      : g(gr), nedge(g)
+		    {
 		      if(start==INVALID) start=NodeIt(g);
 		      for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
 		      while(nedge[start]!=INVALID) {
 		        euler.push_back(nedge[start]);
 		        Node next=g.target(nedge[start]);
 		        ++nedge[start];
 		        start=next;
+		      }
+		    }
 		    ///Arc Conversion
 		    operator Arc() { return euler.empty()?INVALID:euler.front(); }
 		    bool operator==(Invalid) { return euler.empty(); }
 		    bool operator!=(Invalid) { return !euler.empty(); }
 		    ///Next arc of the tour
 		    DiEulerIt &operator++() {
 		      Node s=g.target(euler.front());
 		      euler.pop_front();
 		      //This produces a warning.Strange.
 		      //std::list<Arc>::iterator next=euler.begin();
 		      typename std::list<Arc>::iterator next=euler.begin();
 		      while(nedge[s]!=INVALID) {
 		        euler.insert(next,nedge[s]);
 		        Node n=g.target(nedge[s]);
 		        ++nedge[s];
 		        s=n;
+		      }
 		      return *this;
+		    }
 		    ///Postfix incrementation
 		    ///\warning This incrementation
 		    ///returns an \c Arc, not an \ref DiEulerIt, as one may
 		    ///expect.
 		    Arc operator++(int)
+		    {
 		      Arc e=*this;
 		      ++(*this);
 		      return e;
+		    }
 		  };
 		  ///Euler iterator for graphs.
-		  /// \ingroup graph_prop
+		  /// \ingroup graph_properties
 		  ///This iterator converts to the \c Arc (or \c Edge)
 		  ///type of the digraph and using
 		  ///operator ++, it provides an Euler tour of an undirected
 		  ///digraph (if there exists).
 		  ///
 		  ///For example
 		  ///if the given digraph if Euler (i.e it has only one nontrivial component
 		  ///and the degree of each node is even),
 		  ///the following code will print the arc IDs according to an
 		  ///Euler tour of \c g.
 		  ///\code
 		  ///  for(EulerIt<ListGraph> e(g),e!=INVALID;++e) {
 		  ///    std::cout << g.id(Edge(e)) << std::eol;
 		  ///  }
 		  ///\endcode
 		  ///Although the iterator provides an Euler tour of an graph,
 		  ///it still returns Arcs in order to indicate the direction of the tour.
 		  ///(But Arc will convert to Edges, of course).
 		  ///
 		  ///If \c g is not Euler then the resulted tour will not be full or closed.
 		  ///\sa EulerIt
 		  template<typename GR>
 		  class EulerIt
+		  {
 		    typedef typename GR::Node Node;
 		    typedef typename GR::NodeIt NodeIt;
 		    typedef typename GR::Arc Arc;
 		    typedef typename GR::Edge Edge;
 		    typedef typename GR::ArcIt ArcIt;
 		    typedef typename GR::OutArcIt OutArcIt;
 		    typedef typename GR::InArcIt InArcIt;
 		    const GR &g;
 		    typename GR::template NodeMap<OutArcIt> nedge;
 		    typename GR::template EdgeMap<bool> visited;
 		    std::list<Arc> euler;
 		  public:
 		    ///Constructor
 		    ///\param gr An graph.
 		    ///\param start The starting point of the tour. If it is not given
 		    ///       the tour will start from the first node.
 		    EulerIt(const GR &gr, typename GR::Node start = INVALID)
 		      : g(gr), nedge(g), visited(g, false)
+		    {
 		      if(start==INVALID) start=NodeIt(g);
@@ -183,82 +183,82 @@
+		      }
+		    }
 		    ///Arc Conversion
 		    operator Arc() const { return euler.empty()?INVALID:euler.front(); }
 		    ///Arc Conversion
 		    operator Edge() const { return euler.empty()?INVALID:euler.front(); }
 		    ///\e
 		    bool operator==(Invalid) const { return euler.empty(); }
 		    ///\e
 		    bool operator!=(Invalid) const { return !euler.empty(); }
 		    ///Next arc of the tour
 		    EulerIt &operator++() {
 		      Node s=g.target(euler.front());
 		      euler.pop_front();
 		      typename std::list<Arc>::iterator next=euler.begin();
 		      while(nedge[s]!=INVALID) {
 		        while(nedge[s]!=INVALID && visited[nedge[s]]) ++nedge[s];
 		        if(nedge[s]==INVALID) break;
 		        else {
 		          euler.insert(next,nedge[s]);
 		          visited[nedge[s]]=true;
 		          Node n=g.target(nedge[s]);
 		          ++nedge[s];
 		          s=n;
+		        }
+		      }
 		      return *this;
+		    }
 		    ///Postfix incrementation
 		    ///\warning This incrementation
 		    ///returns an \c Arc, not an \ref EulerIt, as one may
 		    ///expect.
 		    Arc operator++(int)
+		    {
 		      Arc e=*this;
 		      ++(*this);
 		      return e;
+		    }
 		  };
 		  ///Checks if the graph is Eulerian
-		  /// \ingroup graph_prop
+		  /// \ingroup graph_properties
 		  ///Checks if the graph is Eulerian. It works for both directed and undirected
 		  ///graphs.
 		  ///\note By definition, a digraph is called \e Eulerian if
 		  ///and only if it is connected and the number of its incoming and outgoing
 		  ///arcs are the same for each node.
 		  ///Similarly, an undirected graph is called \e Eulerian if
 		  ///and only if it is connected and the number of incident arcs is even
 		  ///for each node. <em>Therefore, there are digraphs which are not Eulerian,
 		  ///but still have an Euler tour</em>.
 		  template<typename GR>
 		#ifdef DOXYGEN
 		  bool
 		#else
 		  typename enable_if<UndirectedTagIndicator<GR>,bool>::type
 		  eulerian(const GR &g)
+		  {
 		    for(typename GR::NodeIt n(g);n!=INVALID;++n)
 		      if(countIncEdges(g,n)%2) return false;
 		    return connected(g);
+		  }
 		  template<class GR>
 		  typename disable_if<UndirectedTagIndicator<GR>,bool>::type
 		#endif
 		  eulerian(const GR &g)
+		  {
 		    for(typename GR::NodeIt n(g);n!=INVALID;++n)
 		      if(countInArcs(g,n)!=countOutArcs(g,n)) return false;
 		    return connected(Undirector<const GR>(g));
+		  }
+		}
 		#endif

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