3 \page graphs How to use graphs
5 The primary data structures of HugoLib 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 \ref ConstGraph concept. This concept does
12 makes it possible to change the graph (i.e. it is not possible to add
13 or delete edges or nodes). Most of the graph algorithms will run on
16 The graphs meeting the \ref ExtendableGraph concept allow node and
17 edge addition. You can also "clear" (i.e. erase all edges and nodes)
20 In case of graphs meeting the full feature \ref ErasableGraph concept
21 you can also erase individual edges and node in arbitrary order.
23 The implemented graph structures are the following.
24 \li \ref hugo::ListGraph "ListGraph" is the most versatile graph class. It meets
25 the ErasableGraph concept and it also have some convenience features.
26 \li \ref hugo::SmartGraph "SmartGraph" is a more memory
27 efficient version of \ref hugo::ListGraph "ListGraph". The
28 price of it is that it only meets the \ref ExtendableGraph concept,
29 so you cannot delete individual edges or nodes.
30 \li \ref hugo::SymListGraph "SymListGraph" and
31 \ref hugo::SymSmartGraph "SymSmartGraph" classes are very similar to
32 \ref hugo::ListGraph "ListGraph" and \ref hugo::SmartGraph "SmartGraph".
33 The difference is that whenever you add a
34 new edge to the graph, it actually adds a pair of oppositely directed edges.
35 They are linked together so it is possible to access the counterpart of an
36 edge. An even more important feature is that using these classes you can also
37 attach data to the edges in such a way that the stored data
38 are shared by the edge pairs.
39 \li \ref hugo::FullGraph "FullGraph"
40 implements a full graph. It is a \ref ConstGraph, so you cannot
41 change the number of nodes once it is constructed. It is extremely memory
42 efficient: it uses constant amount of memory independently from the number of
43 the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and
44 \ref maps "EdgeMap"'s will depend on the number of nodes.
46 \li \ref hugo::NodeSet "NodeSet" implements a graph with no edges. This class
47 can be used as a base class of \ref hugo::EdgeSet "EdgeSet".
48 \li \ref hugo::EdgeSet "EdgeSet" can be used to create a new graph on
49 the edge set of another graph. The base graph can be an arbitrary graph and it
50 is possible to attach several \ref hugo::EdgeSet "EdgeSet"'s to a base graph.
52 \todo Don't we need SmartNodeSet and SmartEdgeSet?
53 \todo Some cross-refs are wrong.
56 The graph structures itself can not store data attached
57 to the edges and nodes. However they all provide
58 \ref maps "map classes"
59 to dynamically attach data the to graph components.
64 The following program demonstrates the basic features of HugoLib's graph
69 #include <hugo/list_graph.h>
75 typedef ListGraph Graph;
78 ListGraph is one of HugoLib's graph classes. It is based on linked lists,
79 therefore iterating throuh its edges and nodes is fast.
82 typedef Graph::Edge Edge;
83 typedef Graph::InEdgeIt InEdgeIt;
84 typedef Graph::OutEdgeIt OutEdgeIt;
85 typedef Graph::EdgeIt EdgeIt;
86 typedef Graph::Node Node;
87 typedef Graph::NodeIt NodeIt;
91 for (int i = 0; i < 3; i++)
94 for (NodeIt i(g); g.valid(i); g.next(i))
95 for (NodeIt j(g); g.valid(j); g.next(j))
96 if (i != j) g.addEdge(i, j);
99 After some convenience typedefs we create a graph and add three nodes to it.
100 Then we add edges to it to form a full graph.
103 std::cout << "Nodes:";
104 for (NodeIt i(g); g.valid(i); g.next(i))
105 std::cout << " " << g.id(i);
106 std::cout << std::endl;
109 Here we iterate through all nodes of the graph. We use a constructor of the
110 node iterator to initialize it to the first node. The next member function is
111 used to step to the next node, and valid is used to check if we have passed the
115 std::cout << "Nodes:";
117 for (g.first(n); n != INVALID; g.next(n))
118 std::cout << " " << g.id(n);
119 std::cout << std::endl;
122 Here you can see an alternative way to iterate through all nodes. Here we use a
123 member function of the graph to initialize the node iterator to the first node
124 of the graph. Using next on the iterator pointing to the last node invalidates
125 the iterator i.e. sets its value to INVALID. Checking for this value is
126 equivalent to using the valid member function.
128 Both of the previous code fragments print out the same:
135 std::cout << "Edges:";
136 for (EdgeIt i(g); g.valid(i); g.next(i))
137 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
138 std::cout << std::endl;
142 Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)
145 We can also iterate through all edges of the graph very similarly. The head and
146 tail member functions can be used to access the endpoints of an edge.
149 NodeIt first_node(g);
151 std::cout << "Out-edges of node " << g.id(first_node) << ":";
152 for (OutEdgeIt i(g, first_node); g.valid(i); g.next(i))
153 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
154 std::cout << std::endl;
156 std::cout << "In-edges of node " << g.id(first_node) << ":";
157 for (InEdgeIt i(g, first_node); g.valid(i); g.next(i))
158 std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";
159 std::cout << std::endl;
163 Out-edges of node 2: (2,0) (2,1)
164 In-edges of node 2: (0,2) (1,2)
167 We can also iterate through the in and out-edges of a node. In the above
168 example we print out the in and out-edges of the first node of the graph.
171 Graph::EdgeMap<int> m(g);
173 for (EdgeIt e(g); g.valid(e); g.next(e))
174 m.set(e, 10 - g.id(e));
176 std::cout << "Id Edge Value" << std::endl;
177 for (EdgeIt e(g); g.valid(e); g.next(e))
178 std::cout << g.id(e) << " (" << g.id(g.tail(e)) << "," << g.id(g.head(e))
179 << ") " << m[e] << std::endl;
192 In generic graph optimization programming graphs are not containers rather
193 incidence structures which are iterable in many ways. HugoLib introduces
194 concepts that allow us to attach containers to graphs. These containers are
197 In the example above we create an EdgeMap which assigns an int value to all
198 edges of the graph. We use the set member function of the map to write values
199 into the map and the operator[] to retrieve them.
201 Here we used the maps provided by the ListGraph class, but you can also write
202 your own maps. You can read more about using maps \ref maps "here".