/** \page basic_concepts Basic concepts \section basic_graph The graph classes The most important classes in LEMON are the graph classes. A 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 whit the rest of the library. The most basic concept is the \ref Graph.
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 it, for example create a edge, assign a value to it through \ref map1 maps. \code lemon::ListGraph::Node new_node = graph.addNode(); \endcode If the graph fits the ErasableGraphComponent concept you also can 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?
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 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 edge 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 fore nodes and a couple for edges - and special classes can have additional iterators too. An example: \code lemon::ListGraph::NodeIt \endcode That is a node iterator. Every iterator type starts whit an name what refers to the iterated object, and ends whit 'It'. LEMON style iterators differs 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.
Let's see these things working together: \code for( ListGraph::NodeIt n(graph); n != INVALID; ++n ) do_useful_things_whit_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.) Very important! The iteration has no defined order. There is absolutely no guaranty 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. */