/*!

 \page graphs How to use graphs

 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".

 */