COIN-OR::LEMON - Graph Library

source: lemon-0.x/doc/graphs.dox @ 1638:4e50ed042394

Last change on this file since 1638:4e50ed042394 was 1638:4e50ed042394, checked in by Akos Ladanyi, 14 years ago

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1/*!
2
3\page graphs Graphs
4
5The primary data structures of LEMON are the graph classes. They all
6provide a node list - edge list interface, i.e. they have
7functionalities to list the nodes and the edges of the graph as well
8as  incoming and outgoing edges of a given node.
9
10
11Each graph should meet the
12\ref lemon::concept::StaticGraph "StaticGraph" concept.
13This concept does not
14make it possible to change the graph (i.e. it is not possible to add
15or delete edges or nodes). Most of the graph algorithms will run on
16these graphs.
17
18The graphs meeting the
19\ref lemon::concept::ExtendableGraph "ExtendableGraph"
20concept allow node and
21edge addition. You can also "clear" such a graph (i.e. erase all edges and nodes ).
22
23In case of graphs meeting the full feature
24\ref lemon::concept::ErasableGraph "ErasableGraph"
25concept
26you can also erase individual edges and nodes in arbitrary order.
27
28The implemented graph structures are the following.
29\li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets
30the \ref lemon::concept::ErasableGraph "ErasableGraph" concept
31and it also has some convenient extra features.
32\li \ref lemon::SmartGraph "SmartGraph" is a more memory
33efficient version of \ref lemon::ListGraph "ListGraph". The
34price of this is that it only meets the
35\ref lemon::concept::ExtendableGraph "ExtendableGraph" concept,
36so you cannot delete individual edges or nodes.
37\li \ref lemon::FullGraph "FullGraph"
38implements a complete graph. It is a
39\ref lemon::concept::StaticGraph "StaticGraph", so you cannot
40change the number of nodes once it is constructed. It is extremely memory
41efficient: it uses constant amount of memory independently from the number of
42the nodes of the graph. Of course, the size of the \ref maps-page "NodeMap"'s and
43\ref maps-page "EdgeMap"'s will depend on the number of nodes.
44
45\li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class
46can be used as a base class of \ref lemon::EdgeSet "EdgeSet".
47\li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on
48the node set of another graph. The base graph can be an arbitrary graph and it
49is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph.
50
51\todo Don't we need SmartNodeSet and SmartEdgeSet?
52\todo Some cross-refs are wrong.
53
54The graph structures themselves can not store data attached
55to the edges and nodes. However they all provide
56\ref maps-page "map classes"
57to dynamically attach data the to graph components.
58
59The following program demonstrates the basic features of LEMON's graph
60structures.
61
62\code
63#include <iostream>
64#include <lemon/list_graph.h>
65
66using namespace lemon;
67
68int main()
69{
70  typedef ListGraph Graph;
71\endcode
72
73ListGraph is one of LEMON's graph classes. It is based on linked lists,
74therefore iterating throuh its edges and nodes is fast.
75
76\code
77  typedef Graph::Edge Edge;
78  typedef Graph::InEdgeIt InEdgeIt;
79  typedef Graph::OutEdgeIt OutEdgeIt;
80  typedef Graph::EdgeIt EdgeIt;
81  typedef Graph::Node Node;
82  typedef Graph::NodeIt NodeIt;
83
84  Graph g;
85 
86  for (int i = 0; i < 3; i++)
87    g.addNode();
88 
89  for (NodeIt i(g); i!=INVALID; ++i)
90    for (NodeIt j(g); j!=INVALID; ++j)
91      if (i != j) g.addEdge(i, j);
92\endcode
93
94After some convenient typedefs we create a graph and add three nodes to it.
95Then we add edges to it to form a complete graph.
96
97\code
98  std::cout << "Nodes:";
99  for (NodeIt i(g); i!=INVALID; ++i)
100    std::cout << " " << g.id(i);
101  std::cout << std::endl;
102\endcode
103
104Here we iterate through all nodes of the graph. We use a constructor of the
105node iterator to initialize it to the first node. The operator++ is used to
106step to the next node. Using operator++ on the iterator pointing to the last
107node invalidates the iterator i.e. sets its value to
108\ref lemon::INVALID "INVALID". This is what we exploit in the stop condition.
109
110The previous code fragment prints out the following:
111
112\code
113Nodes: 2 1 0
114\endcode
115
116\code
117  std::cout << "Edges:";
118  for (EdgeIt i(g); i!=INVALID; ++i)
119    std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
120  std::cout << std::endl;
121\endcode
122
123\code
124Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
125\endcode
126
127We can also iterate through all edges of the graph very similarly. The
128\c target and
129\c source member functions can be used to access the endpoints of an edge.
130
131\code
132  NodeIt first_node(g);
133
134  std::cout << "Out-edges of node " << g.id(first_node) << ":";
135  for (OutEdgeIt i(g, first_node); i!=INVALID; ++i)
136    std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
137  std::cout << std::endl;
138
139  std::cout << "In-edges of node " << g.id(first_node) << ":";
140  for (InEdgeIt i(g, first_node); i!=INVALID; ++i)
141    std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")";
142  std::cout << std::endl;
143\endcode
144
145\code
146Out-edges of node 2: (2,0) (2,1)
147In-edges of node 2: (0,2) (1,2)
148\endcode
149
150We can also iterate through the in and out-edges of a node. In the above
151example we print out the in and out-edges of the first node of the graph.
152
153\code
154  Graph::EdgeMap<int> m(g);
155
156  for (EdgeIt e(g); e!=INVALID; ++e)
157    m.set(e, 10 - g.id(e));
158 
159  std::cout << "Id Edge  Value" << std::endl;
160  for (EdgeIt e(g); e!=INVALID; ++e)
161    std::cout << g.id(e) << "  (" << g.id(g.source(e)) << "," << g.id(g.target(e))
162      << ") " << m[e] << std::endl;
163\endcode
164
165\code
166Id Edge  Value
1674  (0,2) 6
1682  (1,2) 8
1695  (0,1) 5
1700  (2,1) 10
1713  (1,0) 7
1721  (2,0) 9
173\endcode
174
175As we mentioned above, graphs are not containers rather
176incidence structures which are iterable in many ways. LEMON introduces
177concepts that allow us to attach containers to graphs. These containers are
178called maps.
179
180In the example above we create an EdgeMap which assigns an integer value to all
181edges of the graph. We use the set member function of the map to write values
182into the map and the operator[] to retrieve them.
183
184Here we used the maps provided by the ListGraph class, but you can also write
185your own maps. You can read more about using maps \ref maps-page "here".
186
187*/
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