5 \todo Write a new Graphs page. I think it should be contain the Graph,
6 UGraph and BpUGraph concept. It should be describe the iterators and
7 the basic functions and the differences of the implementations.
9 The primary data structures of LEMON are the graph classes. They all
10 provide a node list - edge list interface, i.e. they have
11 functionalities to list the nodes and the edges of the graph as well
12 as incoming and outgoing edges of a given node.
14 Each graph should meet the \ref lemon::concepts::Graph "Graph" concept.
15 This concept does not make it possible to change the graph (i.e. it is
16 not possible to add or delete edges or nodes). Most of the graph
17 algorithms will run on these graphs.
20 In case of graphs meeting the full feature
21 \ref lemon::concepts::ErasableGraph "ErasableGraph"
23 you can also erase individual edges and nodes in arbitrary order.
25 The implemented graph structures are the following.
26 \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets
27 the \ref lemon::concepts::ErasableGraph "ErasableGraph" concept
28 and it also has some convenient extra features.
29 \li \ref lemon::SmartGraph "SmartGraph" is a more memory
30 efficient version of \ref lemon::ListGraph "ListGraph". The
31 price of this is that it only meets the
32 \ref lemon::concepts::ExtendableGraph "ExtendableGraph" concept,
33 so you cannot delete individual edges or nodes.
34 \li \ref lemon::FullGraph "FullGraph"
35 implements a complete graph. It is a
36 \ref lemon::concepts::Graph "Graph", so you cannot
37 change the number of nodes once it is constructed. It is extremely memory
38 efficient: it uses constant amount of memory independently from the number of
39 the nodes of the graph. Of course, the size of the \ref maps-page "NodeMap"'s and
40 \ref maps-page "EdgeMap"'s will depend on the number of nodes.
42 \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class
43 can be used as a base class of \ref lemon::EdgeSet "EdgeSet".
44 \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on
45 the node set of another graph. The base graph can be an arbitrary graph and it
46 is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph.
48 \todo Don't we need SmartNodeSet and SmartEdgeSet?
49 \todo Some cross-refs are wrong.
51 The graph structures themselves can not store data attached
52 to the edges and nodes. However they all provide
53 \ref maps-page "map classes"
54 to dynamically attach data the to graph components.
56 The following program demonstrates the basic features of LEMON's graph
61 #include <lemon/list_graph.h>
63 using namespace lemon;
67 typedef ListGraph Graph;
70 ListGraph is one of LEMON's graph classes. It is based on linked lists,
71 therefore iterating throuh its edges and nodes is fast.
74 typedef Graph::Edge Edge;
75 typedef Graph::InEdgeIt InEdgeIt;
76 typedef Graph::OutEdgeIt OutEdgeIt;
77 typedef Graph::EdgeIt EdgeIt;
78 typedef Graph::Node Node;
79 typedef Graph::NodeIt NodeIt;
83 for (int i = 0; i < 3; i++)
86 for (NodeIt i(g); i!=INVALID; ++i)
87 for (NodeIt j(g); j!=INVALID; ++j)
88 if (i != j) g.addEdge(i, j);
91 After some convenient typedefs we create a graph and add three nodes to it.
92 Then we add edges to it to form a complete graph.
95 std::cout << "Nodes:";
96 for (NodeIt i(g); i!=INVALID; ++i)
97 std::cout << " " << g.id(i);
98 std::cout << std::endl;
101 Here we iterate through all nodes of the graph. We use a constructor of the
102 node iterator to initialize it to the first node. The operator++ is used to
103 step to the next node. Using operator++ on the iterator pointing to the last
104 node invalidates the iterator i.e. sets its value to
105 \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition.
107 The previous code fragment prints out the following:
114 std::cout << "Edges:";
115 for (EdgeIt i(g); i!=INVALID; ++i)
116 std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
117 std::cout << std::endl;
121 Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
124 We can also iterate through all edges of the graph very similarly. The
126 \c source member functions can be used to access the endpoints of an edge.
129 NodeIt first_node(g);
131 std::cout << "Out-edges of node " << g.id(first_node) << ":";
132 for (OutEdgeIt i(g, first_node); i!=INVALID; ++i)
133 std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
134 std::cout << std::endl;
136 std::cout << "In-edges of node " << g.id(first_node) << ":";
137 for (InEdgeIt i(g, first_node); i!=INVALID; ++i)
138 std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
139 std::cout << std::endl;
143 Out-edges of node 2: (2,0) (2,1)
144 In-edges of node 2: (0,2) (1,2)
147 We can also iterate through the in and out-edges of a node. In the above
148 example we print out the in and out-edges of the first node of the graph.
151 Graph::EdgeMap<int> m(g);
153 for (EdgeIt e(g); e!=INVALID; ++e)
154 m.set(e, 10 - g.id(e));
156 std::cout << "Id Edge Value" << std::endl;
157 for (EdgeIt e(g); e!=INVALID; ++e)
158 std::cout << g.id(e) << " (" << g.id(g.source(e)) << "," << g.id(g.target(e))
159 << ") " << m[e] << std::endl;
172 As we mentioned above, graphs are not containers rather
173 incidence structures which are iterable in many ways. LEMON introduces
174 concepts that allow us to attach containers to graphs. These containers are
177 In the example above we create an EdgeMap which assigns an integer value to all
178 edges of the graph. We use the set member function of the map to write values
179 into the map and the operator[] to retrieve them.
181 Here we used the maps provided by the ListGraph class, but you can also write
182 your own maps. You can read more about using maps \ref maps-page "here".