3 \page graphs How to use graphs
5 The primary data structures of LEMON are the graph classes. They all
6 provide a node list - edge list interface, i.e. they have
7 functionalities to list the nodes and the edges of the graph as well
8 as in incoming and outgoing edges of a given node.
11 Each graph should meet the
12 \ref lemon::concept::StaticGraph "StaticGraph" concept.
14 makes it possible to change the graph (i.e. it is not possible to add
15 or delete edges or nodes). Most of the graph algorithms will run on
18 The graphs meeting the
19 \ref lemon::concept::ExtendableGraph "ExtendableGraph"
20 concept allow node and
21 edge addition. You can also "clear" (i.e. erase all edges and nodes)
24 In case of graphs meeting the full feature
25 \ref lemon::concept::ErasableGraph "ErasableGraph"
27 you can also erase individual edges and node in arbitrary order.
29 The implemented graph structures are the following.
30 \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets
31 the \ref lemon::concept::ErasableGraph "ErasableGraph" concept
32 and it also have some convenience features.
33 \li \ref lemon::SmartGraph "SmartGraph" is a more memory
34 efficient version of \ref lemon::ListGraph "ListGraph". The
35 price of it is that it only meets the
36 \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept,
37 so you cannot delete individual edges or nodes.
38 \li \ref lemon::SymListGraph "SymListGraph" and
39 \ref lemon::SymSmartGraph "SymSmartGraph" classes are very similar to
40 \ref lemon::ListGraph "ListGraph" and \ref lemon::SmartGraph "SmartGraph".
41 The difference is that whenever you add a
42 new edge to the graph, it actually adds a pair of oppositely directed edges.
43 They are linked together so it is possible to access the counterpart of an
44 edge. An even more important feature is that using these classes you can also
45 attach data to the edges in such a way that the stored data
46 are shared by the edge pairs.
47 \li \ref lemon::FullGraph "FullGraph"
48 implements a full graph. It is a \ref lemon::concept::StaticGraph, so you cannot
49 change the number of nodes once it is constructed. It is extremely memory
50 efficient: it uses constant amount of memory independently from the number of
51 the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and
52 \ref maps "EdgeMap"'s will depend on the number of nodes.
54 \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class
55 can be used as a base class of \ref lemon::EdgeSet "EdgeSet".
56 \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on
57 the node set of another graph. The base graph can be an arbitrary graph and it
58 is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph.
60 \todo Don't we need SmartNodeSet and SmartEdgeSet?
61 \todo Some cross-refs are wrong.
63 The graph structures itself can not store data attached
64 to the edges and nodes. However they all provide
65 \ref maps "map classes"
66 to dynamically attach data the to graph components.
68 The following program demonstrates the basic features of LEMON's graph
73 #include <lemon/list_graph.h>
75 using namespace lemon;
79 typedef ListGraph Graph;
82 ListGraph is one of LEMON's graph classes. It is based on linked lists,
83 therefore iterating throuh its edges and nodes is fast.
86 typedef Graph::Edge Edge;
87 typedef Graph::InEdgeIt InEdgeIt;
88 typedef Graph::OutEdgeIt OutEdgeIt;
89 typedef Graph::EdgeIt EdgeIt;
90 typedef Graph::Node Node;
91 typedef Graph::NodeIt NodeIt;
95 for (int i = 0; i < 3; i++)
98 for (NodeIt i(g); i!=INVALID; ++i)
99 for (NodeIt j(g); j!=INVALID; ++j)
100 if (i != j) g.addEdge(i, j);
103 After some convenience typedefs we create a graph and add three nodes to it.
104 Then we add edges to it to form a full graph.
107 std::cout << "Nodes:";
108 for (NodeIt i(g); i!=INVALID; ++i)
109 std::cout << " " << g.id(i);
110 std::cout << std::endl;
113 Here we iterate through all nodes of the graph. We use a constructor of the
114 node iterator to initialize it to the first node. The operator++ is used to
115 step to the next node. Using operator++ on the iterator pointing to the last
116 node invalidates the iterator i.e. sets its value to
117 \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition.
119 The previous code fragment prints out the following:
126 std::cout << "Edges:";
127 for (EdgeIt i(g); i!=INVALID; ++i)
128 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
129 std::cout << std::endl;
133 Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
136 We can also iterate through all edges of the graph very similarly. The head and
137 tail member functions can be used to access the endpoints of an edge.
140 NodeIt first_node(g);
142 std::cout << "Out-edges of node " << g.id(first_node) << ":";
143 for (OutEdgeIt i(g, first_node); i!=INVALID; ++i)
144 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
145 std::cout << std::endl;
147 std::cout << "In-edges of node " << g.id(first_node) << ":";
148 for (InEdgeIt i(g, first_node); i!=INVALID; ++i)
149 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
150 std::cout << std::endl;
154 Out-edges of node 2: (2,0) (2,1)
155 In-edges of node 2: (0,2) (1,2)
158 We can also iterate through the in and out-edges of a node. In the above
159 example we print out the in and out-edges of the first node of the graph.
162 Graph::EdgeMap<int> m(g);
164 for (EdgeIt e(g); e!=INVALID; ++e)
165 m.set(e, 10 - g.id(e));
167 std::cout << "Id Edge Value" << std::endl;
168 for (EdgeIt e(g); e!=INVALID; ++e)
169 std::cout << g.id(e) << " (" << g.id(g.tail(e)) << "," << g.id(g.head(e))
170 << ") " << m[e] << std::endl;
183 As we mentioned above, graphs are not containers rather
184 incidence structures which are iterable in many ways. LEMON introduces
185 concepts that allow us to attach containers to graphs. These containers are
188 In the example above we create an EdgeMap which assigns an int value to all
189 edges of the graph. We use the set member function of the map to write values
190 into the map and the operator[] to retrieve them.
192 Here we used the maps provided by the ListGraph class, but you can also write
193 your own maps. You can read more about using maps \ref maps "here".