/*!

 \page graphs How to use graphs

 The primary data structures of HugoLib are the graph classes. They all

 provide a node list - edge list interface, i.e. they have

 functionalities to list the nodes and the edges of the graph as well

 as in incoming and outgoing edges of a given node. 

 Each graph should meet the \ref ConstGraph concept. This concept does

 makes it possible to change the graph (i.e. it is not possible to add

 or delete edges or nodes). Most of the graph algorithms will run on

 these graphs.

 The graphs meeting the \ref ExtendableGraph concept allow node and

 edge addition. You can also "clear" (i.e. erase all edges and nodes)

 such a graph.

 In case of graphs meeting the full feature \ref ErasableGraph concept

 you can also erase individual edges and node in arbitrary order.

 The implemented graph structures are the following.

 \li \ref hugo::ListGraph "ListGraph" is the most versatile graph class. It meets

 the ErasableGraph concept and it also have some convenience features.

 \li \ref hugo::SmartGraph "SmartGraph" is a more memory

 efficient version of \ref hugo::ListGraph "ListGraph". The

 price of it is that it only meets the \ref ExtendableGraph concept,

 so you cannot delete individual edges or nodes.

 \li \ref hugo::SymListGraph "SymListGraph" and

 \ref hugo::SymSmartGraph "SymSmartGraph" classes are very similar to

 \ref hugo::ListGraph "ListGraph" and \ref hugo::SmartGraph "SmartGraph".

 The difference is that whenever you add a

 new edge to the graph, it actually adds a pair of oppositely directed edges.

 They are linked together so it is possible to access the counterpart of an

 edge. An even more important feature is that using these classes you can also

 attach data to the edges in such a way that the stored data

 are shared by the edge pairs. 

 \li \ref hugo::FullGraph "FullGraph"

 implements a full graph. It is a \ref ConstGraph, so you cannot

 change the number of nodes once it is constructed. It is extremely memory

 efficient: it uses constant amount of memory independently from the number of

 the nodes of the graph. Of course, the size of the \ref maps "NodeMap"'s and

 \ref maps "EdgeMap"'s will depend on the number of nodes.

 \li \ref hugo::NodeSet "NodeSet" implements a graph with no edges. This class

 can be used as a base class of \ref hugo::EdgeSet "EdgeSet".

 \li \ref hugo::EdgeSet "EdgeSet" can be used to create a new graph on

 the edge set of another graph. The base graph can be an arbitrary graph and it

 is possible to attach several \ref hugo::EdgeSet "EdgeSet"'s to a base graph.

 \todo Don't we need SmartNodeSet and SmartEdgeSet?

 \todo Some cross-refs are wrong.

 The graph structures itself can not store data attached

 to the edges and nodes. However they all provide

 \ref maps "map classes"

 to dynamically attach data the to graph components.

 The following program demonstrates the basic features of HugoLib's graph

 structures.

 \code

 #include <iostream>

 #include <hugo/list_graph.h>

 using namespace hugo;

 int main()

 {

   typedef ListGraph Graph;

 \endcode

 ListGraph is one of HugoLib's graph classes. It is based on linked lists,

 therefore iterating throuh its edges and nodes is fast.

 \code

   typedef Graph::Edge Edge;

   typedef Graph::InEdgeIt InEdgeIt;

   typedef Graph::OutEdgeIt OutEdgeIt;

   typedef Graph::EdgeIt EdgeIt;

   typedef Graph::Node Node;

   typedef Graph::NodeIt NodeIt;

   Graph g;

   for (int i = 0; i < 3; i++)

     g.addNode();

   for (NodeIt i(g); g.valid(i); g.next(i))

     for (NodeIt j(g); g.valid(j); g.next(j))

       if (i != j) g.addEdge(i, j);

 \endcode

 After some convenience typedefs we create a graph and add three nodes to it.

 Then we add edges to it to form a full graph.

 \code

   std::cout << "Nodes:";

   for (NodeIt i(g); g.valid(i); g.next(i))

     std::cout << " " << g.id(i);

   std::cout << std::endl;

 \endcode

 Here we iterate through all nodes of the graph. We use a constructor of the

 node iterator to initialize it to the first node. The next member function is

 used to step to the next node, and valid is used to check if we have passed the

 last one.

 \code

   std::cout << "Nodes:";

   NodeIt n;

   for (g.first(n); n != INVALID; g.next(n))

     std::cout << " " << g.id(n);

   std::cout << std::endl;

 \endcode

 Here you can see an alternative way to iterate through all nodes. Here we use a

 member function of the graph to initialize the node iterator to the first node

 of the graph. Using next on the iterator pointing to the last node invalidates

 the iterator i.e. sets its value to INVALID. Checking for this value is

 equivalent to using the valid member function.

 Both of the previous code fragments print out the same:

 \code

 Nodes: 2 1 0

 \endcode

 \code

   std::cout << "Edges:";

   for (EdgeIt i(g); g.valid(i); g.next(i))

     std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")";

   std::cout << std::endl;

 \endcode

 \code

 Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0)

 \endcode

 We can also iterate through all edges of the graph very similarly. The head and

 tail member functions can be used to access the endpoints of an edge.

 \code

   NodeIt first_node(g);

   std::cout << "Out-edges of node " << g.id(first_node) << ":";

   for (OutEdgeIt i(g, first_node); g.valid(i); g.next(i))

     std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; 

   std::cout << std::endl;

   std::cout << "In-edges of node " << g.id(first_node) << ":";

   for (InEdgeIt i(g, first_node); g.valid(i); g.next(i))

     std::cout << " (" << g.id(g.tail(i)) << "," << g.id(g.head(i)) << ")"; 

   std::cout << std::endl;

 \endcode

 \code

 Out-edges of node 2: (2,0) (2,1)

 In-edges of node 2: (0,2) (1,2)

 \endcode

 We can also iterate through the in and out-edges of a node. In the above

 example we print out the in and out-edges of the first node of the graph.

 \code

   Graph::EdgeMap<int> m(g);

   for (EdgeIt e(g); g.valid(e); g.next(e))

     m.set(e, 10 - g.id(e));

   std::cout << "Id Edge  Value" << std::endl;

   for (EdgeIt e(g); g.valid(e); g.next(e))

     std::cout << g.id(e) << "  (" << g.id(g.tail(e)) << "," << g.id(g.head(e))

       << ") " << m[e] << std::endl;

 \endcode

 \code

 Id Edge  Value

 4  (0,2) 6

 2  (1,2) 8

 5  (0,1) 5

 0  (2,1) 10

 3  (1,0) 7

 1  (2,0) 9

 \endcode

 In generic graph optimization programming graphs are not containers rather

 incidence structures which are iterable in many ways. HugoLib introduces

 concepts that allow us to attach containers to graphs. These containers are

 called maps.

 In the example above we create an EdgeMap which assigns an int value to all

 edges of the graph. We use the set member function of the map to write values

 into the map and the operator[] to retrieve them.

 Here we used the maps provided by the ListGraph class, but you can also write

 your own maps. You can read more about using maps \ref maps "here".

 */