LEMON/LEMON-official Changeset - r633:7c12061bd271

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Changeset - r633:7c12061bd271

« 630:99a31b

634:114920 »

r633:7c12061bd271

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 $(DOC_PNG_IMAGES)
 			-rm -rf doc/gen-images
 		update-external-tags:
 			wget -O doc/libstdc++.tag.tmp http://gcc.gnu.org/onlinedocs/libstdc++/latest-doxygen/libstdc++.tag && \
 			mv doc/libstdc++.tag.tmp doc/libstdc++.tag || \
 			rm doc/libstdc++.tag.tmp
 		install-html-local: doc/html
 			@$(NORMAL_INSTALL)
 			$(mkinstalldirs) $(DESTDIR)$(htmldir)/docs
 			for p in doc/html/*.{html,css,png,map,gif,tag} ; do \
 			  f="`echo $$p | sed -e 's|^.*/||'`"; \
 			  echo " $(INSTALL_DATA) $$p $(DESTDIR)$(htmldir)/docs/$$f"; \
 			  $(INSTALL_DATA) $$p $(DESTDIR)$(htmldir)/docs/$$f; \
 			done
 		uninstall-local:
 			@$(NORMAL_UNINSTALL)
 			for p in doc/html/*.{html,css,png,map,gif,tag} ; do \
 			  f="`echo $$p | sed -e 's|^.*/||'`"; \
 			  echo " rm -f $(DESTDIR)$(htmldir)/docs/$$f"; \
 			  rm -f $(DESTDIR)$(htmldir)/docs/$$f; \
 			done
 		.PHONY: update-external-tags

doc/groups.dox

Show inline comments

@@ -26,662 +26,662 @@
 		/**
 		@defgroup graphs Graph Structures
 		@ingroup datas
 		\brief Graph structures implemented in LEMON.
 		The implementation of combinatorial algorithms heavily relies on
 		efficient graph implementations. LEMON offers data structures which are
 		planned to be easily used in an experimental phase of implementation studies,
 		and thereafter the program code can be made efficient by small modifications.
 		The most efficient implementation of diverse applications require the
 		usage of different physical graph implementations. These differences
 		appear in the size of graph we require to handle, memory or time usage
 		limitations or in the set of operations through which the graph can be
 		accessed.  LEMON provides several physical graph structures to meet
 		the diverging requirements of the possible users.  In order to save on
 		running time or on memory usage, some structures may fail to provide
 		some graph features like arc/edge or node deletion.
 		Alteration of standard containers need a very limited number of
 		operations, these together satisfy the everyday requirements.
 		In the case of graph structures, different operations are needed which do
 		not alter the physical graph, but gives another view. If some nodes or
 		arcs have to be hidden or the reverse oriented graph have to be used, then
 		this is the case. It also may happen that in a flow implementation
 		the residual graph can be accessed by another algorithm, or a node-set
 		is to be shrunk for another algorithm.
 		LEMON also provides a variety of graphs for these requirements called
 		\ref graph_adaptors "graph adaptors". Adaptors cannot be used alone but only
 		in conjunction with other graph representations.
 		You are free to use the graph structure that fit your requirements
 		the best, most graph algorithms and auxiliary data structures can be used
 		with any graph structure.
 		<b>See also:</b> \ref graph_concepts "Graph Structure Concepts".
 		*/
 		/**
 		@defgroup graph_adaptors Adaptor Classes for Graphs
 		@ingroup graphs
 		\brief Adaptor classes for digraphs and graphs
 		This group contains several useful adaptor classes for digraphs and graphs.
 		The main parts of LEMON are the different graph structures, generic
 		graph algorithms, graph concepts, which couple them, and graph
 		adaptors. While the previous notions are more or less clear, the
 		latter one needs further explanation. Graph adaptors are graph classes
 		which serve for considering graph structures in different ways.
 		A short example makes this much clearer.  Suppose that we have an
 		instance \c g of a directed graph type, say ListDigraph and an algorithm
 		\code
 		template <typename Digraph>
 		int algorithm(const Digraph&);
 		\endcode
 		is needed to run on the reverse oriented graph.  It may be expensive
 		(in time or in memory usage) to copy \c g with the reversed
 		arcs.  In this case, an adaptor class is used, which (according
 		to LEMON \ref concepts::Digraph "digraph concepts") works as a digraph.
 		The adaptor uses the original digraph structure and digraph operations when
 		methods of the reversed oriented graph are called.  This means that the adaptor
 		have minor memory usage, and do not perform sophisticated algorithmic
 		actions.  The purpose of it is to give a tool for the cases when a
 		graph have to be used in a specific alteration.  If this alteration is
 		obtained by a usual construction like filtering the node or the arc set or
 		considering a new orientation, then an adaptor is worthwhile to use.
 		To come back to the reverse oriented graph, in this situation
 		\code
 		template<typename Digraph> class ReverseDigraph;
 		\endcode
 		template class can be used. The code looks as follows
 		\code
 		ListDigraph g;
 		ReverseDigraph<ListDigraph> rg(g);
 		int result = algorithm(rg);
 		\endcode
 		During running the algorithm, the original digraph \c g is untouched.
 		This techniques give rise to an elegant code, and based on stable
 		graph adaptors, complex algorithms can be implemented easily.
 		In flow, circulation and matching problems, the residual
 		graph is of particular importance. Combining an adaptor implementing
 		this with shortest path algorithms or minimum mean cycle algorithms,
 		a range of weighted and cardinality optimization algorithms can be
 		obtained. For other examples, the interested user is referred to the
 		detailed documentation of particular adaptors.
 		The behavior of graph adaptors can be very different. Some of them keep
 		capabilities of the original graph while in other cases this would be
 		meaningless. This means that the concepts that they meet depend
 		on the graph adaptor, and the wrapped graph.
 		For example, if an arc of a reversed digraph is deleted, this is carried
 		out by deleting the corresponding arc of the original digraph, thus the
 		adaptor modifies the original digraph.
 		However in case of a residual digraph, this operation has no sense.
 		Let us stand one more example here to simplify your work.
 		ReverseDigraph has constructor
 		\code
 		ReverseDigraph(Digraph& digraph);
 		\endcode
 		This means that in a situation, when a <tt>const %ListDigraph&</tt>
 		reference to a graph is given, then it have to be instantiated with
 		<tt>Digraph=const %ListDigraph</tt>.
 		\code
 		int algorithm1(const ListDigraph& g) {
 		  ReverseDigraph<const ListDigraph> rg(g);
 		  return algorithm2(rg);
+		}
 		\endcode
 		*/
 		/**
 		@defgroup semi_adaptors Semi-Adaptor Classes for Graphs
 		@ingroup graphs
 		\brief Graph types between real graphs and graph adaptors.
 		This group contains some graph types between real graphs and graph adaptors.
 		These classes wrap graphs to give new functionality as the adaptors do it.
 		On the other hand they are not light-weight structures as the adaptors.
 		*/
 		/**
 		@defgroup maps Maps
 		@ingroup datas
 		\brief Map structures implemented in LEMON.
 		This group contains the map structures implemented in LEMON.
 		LEMON provides several special purpose maps and map adaptors that e.g. combine
 		new maps from existing ones.
 		<b>See also:</b> \ref map_concepts "Map Concepts".
 		*/
 		/**
 		@defgroup graph_maps Graph Maps
 		@ingroup maps
 		\brief Special graph-related maps.
 		This group contains maps that are specifically designed to assign
 		values to the nodes and arcs/edges of graphs.
 		If you are looking for the standard graph maps (\c NodeMap, \c ArcMap,
 		\c EdgeMap), see the \ref graph_concepts "Graph Structure Concepts".
 		*/
 		/**
 		\defgroup map_adaptors Map Adaptors
 		\ingroup maps
 		\brief Tools to create new maps from existing ones
 		This group contains map adaptors that are used to create "implicit"
 		maps from other maps.
 		Most of them are \ref concepts::ReadMap "read-only maps".
 		They can make arithmetic and logical operations between one or two maps
 		(negation, shifting, addition, multiplication, logical 'and', 'or',
 		'not' etc.) or e.g. convert a map to another one of different Value type.
 		The typical usage of this classes is passing implicit maps to
 		algorithms.  If a function type algorithm is called then the function
 		type map adaptors can be used comfortable. For example let's see the
 		usage of map adaptors with the \c graphToEps() function.
 		\code
 		  Color nodeColor(int deg) {
 		    if (deg >= 2) {
 		      return Color(0.5, 0.0, 0.5);
 		    } else if (deg == 1) {
 		      return Color(1.0, 0.5, 1.0);
 		    } else {
 		      return Color(0.0, 0.0, 0.0);
+		    }
+		  }
 		  Digraph::NodeMap<int> degree_map(graph);
 		  graphToEps(graph, "graph.eps")
 		    .coords(coords).scaleToA4().undirected()
 		    .nodeColors(composeMap(functorToMap(nodeColor), degree_map))
 		    .run();
 		\endcode
 		The \c functorToMap() function makes an \c int to \c Color map from the
 		\c nodeColor() function. The \c composeMap() compose the \c degree_map
 		and the previously created map. The composed map is a proper function to
 		get the color of each node.
 		The usage with class type algorithms is little bit harder. In this
 		case the function type map adaptors can not be used, because the
 		function map adaptors give back temporary objects.
 		\code
 		  Digraph graph;
 		  typedef Digraph::ArcMap<double> DoubleArcMap;
 		  DoubleArcMap length(graph);
 		  DoubleArcMap speed(graph);
 		  typedef DivMap<DoubleArcMap, DoubleArcMap> TimeMap;
 		  TimeMap time(length, speed);
 		  Dijkstra<Digraph, TimeMap> dijkstra(graph, time);
 		  dijkstra.run(source, target);
 		\endcode
 		We have a length map and a maximum speed map on the arcs of a digraph.
 		The minimum time to pass the arc can be calculated as the division of
 		the two maps which can be done implicitly with the \c DivMap template
 		class. We use the implicit minimum time map as the length map of the
 		\c Dijkstra algorithm.
 		*/
 		/**
 		@defgroup matrices Matrices
 		@ingroup datas
 		\brief Two dimensional data storages implemented in LEMON.
 		This group contains two dimensional data storages implemented in LEMON.
 		*/
 		/**
 		@defgroup paths Path Structures
 		@ingroup datas
 		\brief %Path structures implemented in LEMON.
 		This group contains the path structures implemented in LEMON.
 		LEMON provides flexible data structures to work with paths.
 		All of them have similar interfaces and they can be copied easily with
 		assignment operators and copy constructors. This makes it easy and
 		efficient to have e.g. the Dijkstra algorithm to store its result in
 		any kind of path structure.
 		\sa lemon::concepts::Path
 		*/
 		/**
 		@defgroup auxdat Auxiliary Data Structures
 		@ingroup datas
 		\brief Auxiliary data structures implemented in LEMON.
 		This group contains some data structures implemented in LEMON in
 		order to make it easier to implement combinatorial algorithms.
 		*/
 		/**
 		@defgroup algs Algorithms
 		\brief This group contains the several algorithms
 		implemented in LEMON.
 		This group contains the several algorithms
 		implemented in LEMON.
 		*/
 		/**
 		@defgroup search Graph Search
 		@ingroup algs
 		\brief Common graph search algorithms.
 		This group contains the common graph search algorithms, namely
 		\e breadth-first \e search (BFS) and \e depth-first \e search (DFS).
 		*/
 		/**
 		@defgroup shortest_path Shortest Path Algorithms
 		@ingroup algs
 		\brief Algorithms for finding shortest paths.
 		This group contains the algorithms for finding shortest paths in digraphs.
 		 - \ref Dijkstra algorithm for finding shortest paths from a source node
 		   when all arc lengths are non-negative.
 		 - \ref BellmanFord "Bellman-Ford" algorithm for finding shortest paths
 		   from a source node when arc lenghts can be either positive or negative,
 		   but the digraph should not contain directed cycles with negative total
 		   length.
 		 - \ref FloydWarshall "Floyd-Warshall" and \ref Johnson "Johnson" algorithms
 		   for solving the \e all-pairs \e shortest \e paths \e problem when arc
 		   lenghts can be either positive or negative, but the digraph should
 		   not contain directed cycles with negative total length.
 		 - \ref Suurballe A successive shortest path algorithm for finding
 		   arc-disjoint paths between two nodes having minimum total length.
 		*/
 		/**
 		@defgroup max_flow Maximum Flow Algorithms
 		@ingroup algs
 		\brief Algorithms for finding maximum flows.
 		This group contains the algorithms for finding maximum flows and
 		feasible circulations.
 		The \e maximum \e flow \e problem is to find a flow of maximum value between
 		a single source and a single target. Formally, there is a \f$G=(V,A)\f$
 		digraph, a \f$cap:A\rightarrow\mathbf{R}^+_0\f$ capacity function and
 		\f$s, t \in V\f$ source and target nodes.
 		A maximum flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of the
 		following optimization problem.
 		\f[ \max\sum_{a\in\delta_{out}(s)}f(a) - \sum_{a\in\delta_{in}(s)}f(a) \f]
 		\f[ \sum_{a\in\delta_{out}(v)} f(a) = \sum_{a\in\delta_{in}(v)} f(a)
 		    \qquad \forall v\in V\setminus\{s,t\} \f]
 		\f[ 0 \leq f(a) \leq cap(a) \qquad \forall a\in A \f]
 		LEMON contains several algorithms for solving maximum flow problems:
 		- \ref EdmondsKarp Edmonds-Karp algorithm.
 		- \ref Preflow Goldberg-Tarjan's preflow push-relabel algorithm.
 		- \ref DinitzSleatorTarjan Dinitz's blocking flow algorithm with dynamic trees.
 		- \ref GoldbergTarjan Preflow push-relabel algorithm with dynamic trees.
 		In most cases the \ref Preflow "Preflow" algorithm provides the
 		fastest method for computing a maximum flow. All implementations
 		provides functions to also query the minimum cut, which is the dual
 		problem of the maximum flow.
 		*/
 		/**
 		@defgroup min_cost_flow Minimum Cost Flow Algorithms
 		@ingroup algs
 		\brief Algorithms for finding minimum cost flows and circulations.
 		This group contains the algorithms for finding minimum cost flows and
 		circulations.
 		The \e minimum \e cost \e flow \e problem is to find a feasible flow of
 		minimum total cost from a set of supply nodes to a set of demand nodes
 		in a network with capacity constraints and arc costs.
 		Formally, let \f$G=(V,A)\f$ be a digraph,
 		\f$lower, upper: A\rightarrow\mathbf{Z}^+_0\f$ denote the lower and
 		upper bounds for the flow values on the arcs,
 		\f$cost: A\rightarrow\mathbf{Z}^+_0\f$ denotes the cost per unit flow
 		on the arcs, and
 		\f$supply: V\rightarrow\mathbf{Z}\f$ denotes the supply/demand values
 		of the nodes.
 		A minimum cost flow is an \f$f:A\rightarrow\mathbf{R}^+_0\f$ solution of
 		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
 		  matching in bipartite graphs.
 		- \ref MaxMatching Edmond's blossom shrinking algorithm for calculating
 		  maximum cardinality matching in general graphs.
 		- \ref MaxWeightedMatching Edmond's blossom shrinking algorithm for calculating
 		  maximum weighted matching in general graphs.
 		- \ref MaxWeightedPerfectMatching
 		  Edmond's blossom shrinking algorithm for calculating maximum weighted
 		  perfect matching in general graphs.
 		\image html bipartite_matching.png
 		\image latex bipartite_matching.eps "Bipartite Matching" width=\textwidth
 		*/
 		/**
 		@defgroup spantree Minimum Spanning Tree Algorithms
 		@ingroup algs
 		\brief Algorithms for finding a minimum cost spanning tree in a graph.
 		This group contains the algorithms for finding a minimum cost spanning
 		tree in a graph.
 		*/
 		/**
 		@defgroup auxalg Auxiliary Algorithms
 		@ingroup algs
 		\brief Auxiliary algorithms implemented in LEMON.
 		This group contains some algorithms implemented in LEMON
 		in order to make it easier to implement complex algorithms.
 		*/
 		/**
 		@defgroup approx Approximation Algorithms
 		@ingroup algs
 		\brief Approximation algorithms.
 		This group contains the approximation and heuristic algorithms
 		implemented in LEMON.
 		*/
 		/**
 		@defgroup gen_opt_group General Optimization Tools
 		\brief This group contains some general optimization frameworks
 		implemented in LEMON.
 		This group contains some general optimization frameworks
 		implemented in LEMON.
 		*/
 		/**
 		@defgroup lp_group Lp and Mip Solvers
 		@ingroup gen_opt_group
 		\brief Lp and Mip solver interfaces for LEMON.
 		This group contains Lp and Mip solver interfaces for LEMON. The
 		various LP solvers could be used in the same manner with this
 		interface.
 		*/
 		/**
 		@defgroup lp_utils Tools for Lp and Mip Solvers
 		@ingroup lp_group
 		\brief Helper tools to the Lp and Mip solvers.
 		This group adds some helper tools to general optimization framework
 		implemented in LEMON.
 		*/
 		/**
 		@defgroup metah Metaheuristics
 		@ingroup gen_opt_group
 		\brief Metaheuristics for LEMON library.
 		This group contains some metaheuristic optimization tools.
 		*/
 		/**
 		@defgroup utils Tools and Utilities
 		\brief Tools and utilities for programming in LEMON
 		Tools and utilities for programming in LEMON.
 		*/
 		/**
 		@defgroup gutils Basic Graph Utilities
 		@ingroup utils
 		\brief Simple basic graph utilities.
 		This group contains some simple basic graph utilities.
 		*/
 		/**
 		@defgroup misc Miscellaneous Tools
 		@ingroup utils
 		\brief Tools for development, debugging and testing.
 		This group contains several useful tools for development,
 		debugging and testing.
 		*/
 		/**
 		@defgroup timecount Time Measuring and Counting
 		@ingroup misc
 		\brief Simple tools for measuring the performance of algorithms.
 		This group contains simple tools for measuring the performance
 		of algorithms.
 		*/
 		/**
 		@defgroup exceptions Exceptions
 		@ingroup utils
 		\brief Exceptions defined in LEMON.
 		This group contains the exceptions defined in LEMON.
 		*/
 		/**
 		@defgroup io_group Input-Output
 		\brief Graph Input-Output methods
 		This group contains the tools for importing and exporting graphs
 		and graph related data. Now it supports the \ref lgf-format
 		"LEMON Graph Format", the \c DIMACS format and the encapsulated
 		postscript (EPS) format.
 		*/
 		/**
 		@defgroup lemon_io LEMON Graph Format
 		@ingroup io_group
 		\brief Reading and writing LEMON Graph Format.
 		This group contains methods for reading and writing
 		\ref lgf-format "LEMON Graph Format".
 		*/
 		/**
 		@defgroup eps_io Postscript Exporting
 		@ingroup io_group
 		\brief General \c EPS drawer and graph exporter
 		This group contains general \c EPS drawing methods and special
 		graph exporting tools.
 		*/
 		/**
 		@defgroup dimacs_group DIMACS format
 		@ingroup io_group
 		\brief Read and write files in DIMACS format
 		Tools to read a digraph from or write it to a file in DIMACS format data.
 		*/
 		/**
 		@defgroup nauty_group NAUTY Format
 		@ingroup io_group
 		\brief Read \e Nauty format
 		Tool to read graphs from \e Nauty format data.
 		*/
 		/**
 		@defgroup concept Concepts
 		\brief Skeleton classes and concept checking classes
 		This group contains the data/algorithm skeletons and concept checking
 		classes implemented in LEMON.
 		The purpose of the classes in this group is fourfold.
 		- These classes contain the documentations of the %concepts. In order
 		  to avoid document multiplications, an implementation of a concept
 		  simply refers to the corresponding concept class.
 		- These classes declare every functions, <tt>typedef</tt>s etc. an
 		  implementation of the %concepts should provide, however completely
 		  without implementations and real data structures behind the
 		  interface. On the other hand they should provide nothing else. All
 		  the algorithms working on a data structure meeting a certain concept
 		  should compile with these classes. (Though it will not run properly,
 		  of course.) In this way it is easily to check if an algorithm
 		  doesn't use any extra feature of a certain implementation.
 		- The concept descriptor classes also provide a <em>checker class</em>
 		  that makes it possible to check whether a certain implementation of a
 		  concept indeed provides all the required features.
 		- Finally, They can serve as a skeleton of a new implementation of a concept.
 		*/
 		/**
 		@defgroup graph_concepts Graph Structure Concepts
 		@ingroup concept
 		\brief Skeleton and concept checking classes for graph structures
 		This group contains the skeletons and concept checking classes of LEMON's
 		graph structures and helper classes used to implement these.
 		*/
 		/**
 		@defgroup map_concepts Map Concepts
 		@ingroup concept
 		\brief Skeleton and concept checking classes for maps
 		This group contains the skeletons and concept checking classes of maps.
 		*/
 		/**
 		\anchor demoprograms
 		@defgroup demos Demo Programs
 		Some demo programs are listed here. Their full source codes can be found in
 		the \c demo subdirectory of the source tree.
 		In order to compile them, use the <tt>make demo</tt> or the
 		<tt>make check</tt> commands.
 		*/
 		/**
 		@defgroup tools Standalone Utility Applications
 		Some utility applications are listed here.
 		The standard compilation procedure (<tt>./configure;make</tt>) will compile
 		them, as well.
 		*/
+		}

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;
+		      }
 		    private:
 		      Iterator _it;
 		    };
 		    template <typename Digraph, typename Map>
 		    struct FillMapVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Map::Value Value;
 		      FillMapVisitor(Map& map, Value& value)
 		        : _map(map), _value(value) {}
 		      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;
 		    RVisitor rvisitor(rgraph, cutMap, cutNum);
 		    DfsVisit<RDigraph, RVisitor> rdfs(rgraph, rvisitor);
 		    rdfs.init();
 		    for (RIterator it = nodes.rbegin(); it != nodes.rend(); ++it) {
 		      if (!rdfs.reached(*it)) {
 		        rdfs.addSource(*it);
 		        rdfs.start();
+		      }
+		    }
 		    return cutNum;
+		  }
 		  namespace _connectivity_bits {
 		    template <typename Digraph>
 		    class CountBiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
 		      CountBiNodeConnectedComponentsVisitor(const Digraph& graph, int &compNum)
 		        : _graph(graph), _compNum(compNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap.set(node, INVALID);
+		      }
 		      void reach(const Node& node) {
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        ++_num;
+		      }
 		      void discover(const Arc& edge) {
 		        _predMap.set(_graph.target(edge), _graph.source(edge));
+		      }
 		      void examine(const Arc& edge) {
 		        if (_graph.source(edge) == _graph.target(edge) &&
 		            _graph.direction(edge)) {
 		          ++_compNum;
 		          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)]) {
 		          ++_compNum;
+		        }
+		      }
 		    private:
 		      const Digraph& _graph;
 		      int& _compNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Node> _predMap;
 		      int _num;
 		    };
 		    template <typename Digraph, typename ArcMap>
 		    class BiNodeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
 		      BiNodeConnectedComponentsVisitor(const Digraph& graph,
 		                                       ArcMap& compMap, int &compNum)
 		        : _graph(graph), _compMap(compMap), _compNum(compNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap.set(node, INVALID);
+		      }
 		      void reach(const Node& node) {
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        ++_num;
+		      }
 		      void discover(const Arc& edge) {
 		        Node target = _graph.target(edge);
 		        _predMap.set(target, edge);
 		        _edgeStack.push(edge);
+		      }
 		      void examine(const Arc& edge) {
 		        Node source = _graph.source(edge);
 		        Node target = _graph.target(edge);
 		        if (source == target && _graph.direction(edge)) {
 		          _compMap.set(edge, _compNum);
 		          ++_compNum;
 		          return;
+		        }
 		        if (_numMap[target] < _numMap[source]) {
 		          if (_predMap[source] != _graph.oppositeArc(edge)) {
 		            _edgeStack.push(edge);
+		          }
+		        }
 		        if (_predMap[source] != INVALID &&
 		            target == _graph.source(_predMap[source])) {
 		          return;
+		        }
 		        if (_retMap[source] > _numMap[target]) {
 		          _retMap.set(source, _numMap[target]);
+		        }
+		      }
 		      void backtrack(const Arc& edge) {
 		        Node source = _graph.source(edge);
 		        Node target = _graph.target(edge);
 		        if (_retMap[source] > _retMap[target]) {
 		          _retMap.set(source, _retMap[target]);
+		        }
 		        if (_numMap[source] <= _retMap[target]) {
 		          while (_edgeStack.top() != edge) {
 		            _compMap.set(_edgeStack.top(), _compNum);
 		            _edgeStack.pop();
+		          }
 		          _compMap.set(edge, _compNum);
 		          _edgeStack.pop();
 		          ++_compNum;
+		        }
+		      }
 		    private:
 		      const Digraph& _graph;
 		      ArcMap& _compMap;
 		      int& _compNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Arc> _predMap;
 		      std::stack<Edge> _edgeStack;
 		      int _num;
 		    };
 		    template <typename Digraph, typename NodeMap>
 		    class BiNodeConnectedCutNodesVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
 		      BiNodeConnectedCutNodesVisitor(const Digraph& graph, NodeMap& cutMap,
 		                                     int& cutNum)
 		        : _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap.set(node, INVALID);
 		        rootCut = false;
+		      }
 		      void reach(const Node& node) {
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        ++_num;
+		      }
 		      void discover(const Arc& edge) {
 		        _predMap.set(_graph.target(edge), _graph.source(edge));
+		      }
 		      void examine(const Arc& edge) {
 		        if (_graph.source(edge) == _graph.target(edge) &&
 		            _graph.direction(edge)) {
 		          if (!_cutMap[_graph.source(edge)]) {
 		            _cutMap.set(_graph.source(edge), true);
 		            ++_cutNum;
+		          }
 		          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;
 		      CountBiEdgeConnectedComponentsVisitor(const Digraph& graph, int &compNum)
 		        : _graph(graph), _compNum(compNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap.set(node, INVALID);
+		      }
 		      void reach(const Node& node) {
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        ++_num;
+		      }
 		      void leave(const Node& node) {
 		        if (_numMap[node] <= _retMap[node]) {
 		          ++_compNum;
+		        }
+		      }
 		      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;
 		      int& _compNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Arc> _predMap;
 		      int _num;
 		    };
 		    template <typename Digraph, typename NodeMap>
 		    class BiEdgeConnectedComponentsVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
 		      BiEdgeConnectedComponentsVisitor(const Digraph& graph,
 		                                       NodeMap& compMap, int &compNum)
 		        : _graph(graph), _compMap(compMap), _compNum(compNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap.set(node, INVALID);
+		      }
 		      void reach(const Node& node) {
 		        _numMap.set(node, _num);
 		        _retMap.set(node, _num);
 		        _nodeStack.push(node);
 		        ++_num;
+		      }
 		      void leave(const Node& node) {
 		        if (_numMap[node] <= _retMap[node]) {
 		          while (_nodeStack.top() != node) {
 		            _compMap.set(_nodeStack.top(), _compNum);
 		            _nodeStack.pop();
+		          }
 		          _compMap.set(node, _compNum);
 		          _nodeStack.pop();
 		          ++_compNum;
+		        }
+		      }
 		      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;
 		      NodeMap& _compMap;
 		      int& _compNum;
 		      typename Digraph::template NodeMap<int> _numMap;
 		      typename Digraph::template NodeMap<int> _retMap;
 		      typename Digraph::template NodeMap<Arc> _predMap;
 		      std::stack<Node> _nodeStack;
 		      int _num;
 		    };
 		    template <typename Digraph, typename ArcMap>
 		    class BiEdgeConnectedCutEdgesVisitor : public DfsVisitor<Digraph> {
 		    public:
 		      typedef typename Digraph::Node Node;
 		      typedef typename Digraph::Arc Arc;
 		      typedef typename Digraph::Edge Edge;
 		      BiEdgeConnectedCutEdgesVisitor(const Digraph& graph,
 		                                     ArcMap& cutMap, int &cutNum)
 		        : _graph(graph), _cutMap(cutMap), _cutNum(cutNum),
 		          _numMap(graph), _retMap(graph), _predMap(graph), _num(0) {}
 		      void start(const Node& node) {
 		        _predMap[node] = INVALID;
+		      }
 		      void reach(const Node& node) {
 		        _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>
 		  bool parallelFree(const Digraph& digraph) {
 		    typename Digraph::template NodeMap<bool> reached(digraph, false);
 		    for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
 		      for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 		        if (reached[digraph.target(a)]) return false;
 		        reached.set(digraph.target(a), true);
+		      }
 		      for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 		        reached.set(digraph.target(a), false);
+		      }
+		    }
 		    return true;
+		  }
 		  /// \brief Returns true when there are not loop edges and parallel
 		  /// edges in the graph.
 		  ///
 		  /// Returns true when there are not loop edges and parallel edges in
 		  /// the graph.
 		  template <typename Digraph>
 		  bool simpleDigraph(const Digraph& digraph) {
 		    typename Digraph::template NodeMap<bool> reached(digraph, false);
 		    for (typename Digraph::NodeIt n(digraph); n != INVALID; ++n) {
 		      reached.set(n, true);
 		      for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 		        if (reached[digraph.target(a)]) return false;
 		        reached.set(digraph.target(a), true);
+		      }
 		      for (typename Digraph::OutArcIt a(digraph, n); a != INVALID; ++a) {
 		        reached.set(digraph.target(a), false);
+		      }
 		      reached.set(n, false);
+		    }
 		    return true;
+		  }
 		} //namespace lemon
 		#endif //LEMON_CONNECTIVITY_H

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);
 		      for(NodeIt n(g);n!=INVALID;++n) nedge[n]=OutArcIt(g,n);
 		      while(nedge[start]!=INVALID) {
 		        euler.push_back(nedge[start]);
 		        visited[nedge[start]]=true;
 		        Node next=g.target(nedge[start]);
 		        ++nedge[start];
 		        start=next;
 		        while(nedge[start]!=INVALID && visited[nedge[start]]) ++nedge[start];
+		      }
+		    }
 		    ///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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