/**

\page basic_concepts Basic concepts

\section basic_graph The graph classes

The most important classes in LEMON are the graph classes. An instance of a graph

class is the representation of the mathematical graph. It holds the topology and

every structural information of the graph. The structural manipulations are also

provided by the graph object. There is no universal graph class instead we have

different classes for different purposes. They can differ in many ways, but all

have to satisfy one or more \ref concept "graph concepts" which are standardized

interfaces to work with the rest of the library. The most basic concept is the

\ref Graph.<br>

A good example is the \ref ListGraph which we already know from Hello World and

will be used in our examples as well.

One main advantage of the templates are, that you can write your own graph classes.

As long as they provide the interface a concept is defining all the LEMON algorithms

and classes will work with it properly - no representation or implementation is

written into stone.

\subsection basic_node Nodes

To refer to a node of a graph we need some kind of typed variable. Graph classes

have the Node public type for this purpose. Stacking by the last example:

\code lemon::ListGraph::Node \endcode

If the graph fits the ExtendableGraphComponent concept, then you can add new nodes

to the graph with the addNode() member function. It returns the newly added node

(as value). So if you need the new node to do something useful with, for example

create an edge, assign a value to it through \ref map1 maps.

\code lemon::ListGraph::Node  new_node = graph.addNode(); \endcode

If the graph fits into the ErasableGraphComponent concept you can also remove nodes

from the graph with the erase() member function.

\code graph.erase( new_node ); \endcode

You don't have to store every node in a variable, you can access individual nodes

with node iterators discussed in the next section. But how do you know which

node is which?<br>

The graph class has the id( Node n ) member function providing an unique identifier

assigned to every node.

\subsection basic_edge Edges

An Edge is what you think it is. It goes from one node to another node (they can

be identical if the edge is a loop). If the graph class is directed, the Edge is directed too. Otherwise

the edge is considered undirected and called UEdge.

\code lemon::ListUGraph::UEdge \endcode

The addEdge() member function will create a new edge. It has two arguments, the

source node and the target node. The graph class must be extendable.

\code lemon::ListGraph::Edge  new_edge = graph.addEdge( src_node, trg_node ); \endcode

You can handle edges similar as nodes. The erase() member function has an edge taking

overload too.

You can ask for the source or target node of the edge by the corresponding member

functions:

\code

graph.source( new_edge );

lemon::ListGraph::Node  n = graph.target( new_edge ); \endcode

These functions are always legal even if the graph is undirected. UEdge has a

default direction.

\section basic_iterators Iterators

Graphs are some kind of containers. And as you expect they have iterator types.

One for nodes and a couple for edges - and special classes can have additional

iterators too. An example:

\code lemon::ListGraph::NodeIt \endcode

This is a node iterator. Every iterator type starts with a name that refers to

the iterated object, and ends with 'It'.

LEMON style iterators differ from \c stl or \c boost iterators in a very tasty

way. A graph has no begin or end - or at least a generic graph class has none.

If by some topology you could pick a good begin node, it would be misleading and

incorrect. A LEMON style iterator must be initialized at construction time.

The constructor takes the needed parameters - by a node iterator it's the graph

object. And will be compared to the lemon::INVALID to check if it's still valid.

Every iterator can be compared to INVALID. No \c begin() or \c end() needed.<br>

Let's see these things working together:

\code

for( ListGraph::NodeIt n(graph); n != INVALID; ++n )

    do_useful_things_with_node(n);

\endcode

Note that the function \c do_useful_things_with_node() expects a Node type argument

ad we just gave him the iterator. LEMON style iterators must provide "on demand

dereferencing". For example a NodeIt can be used everywhere a Node could. (In some

graph classes Node is the base class of NodeIt. But in other cases this is implemented

through typecast operator.)

<b>Very important!</b> The iteration has no defined order. There is absolutely no

warranty that the next time the iteration will give us the nodes in the same order.

Don't use this order to identify nodes! Use the \c id() member function of the

graph class described above. (There is a powerful technique using maps right in

the next page.)

The \ref EdgeIt works exactly the same - nothing more to say. But there are \ref InEdgeIt

and \ref OutEdgeIt by directed graphs and \ref IncEdgeIt by undirected graphs.

They take two arguments. The first is a graph, the second is certain node of the

graph. InEdgeIt iterates on the incoming edges of that node and OutEdgeIt does it

on the outgoing edges. The IncEdgeIt of course iterates every edge connecting to

the given node.

\code

for( ListGraph::NodeIt n(graph); n != INVALID; ++n ) {

  int in = 0, out = 0;

  for( ListGraph::InEdgeIt e(graph,n); e != INVALID; ++e ) ++in;

  for( ListGraph::OutEdgeIt e(graph,n); e != INVALID; ++e ) ++out;

  std::cout << "#" << graph.id(n) << " node has " << in << " incoming and "

    << out << "outgoing edges." << std::endl;

}

\endcode

\section basic_ListGraph ListGraph - a versatile directed graph

As you see ListGraph satisfies most of the basic concepts and ideal for general

graph representations. It has an undirected version too: ListUGraph.

*/