2 \page basic_concepts Basic concepts
4 \section basic_graph The graph classes
5 The most important classes in LEMON are the graph classes. A instance of a graph
6 class is the representation of the mathematical graph. It holds the topology and
7 every structural information of the graph. The structural manipulations are also
8 provided by the graph object. There is no universal graph class instead we have
9 different classes for different purposes. They can differ in many ways, but all
10 have to satisfy one or more \ref concept "graph concepts" which are standardized
11 interfaces to work whit the rest of the library. The most basic concept is the
13 A good example is the \ref ListGraph which we already know from Hello World and
14 will be used in our examples as well.
16 One main advantage of the templates are, that you can write your own graph classes.
17 As long as they provide the interface a concept is defining all the LEMON algorithms
18 and classes will work with it properly - no representation or implementation is
22 \subsection basic_node Nodes
23 To refer to a node of a graph we need some kind of typed variable. Graph classes
24 have the Node public type for this purpose. Stacking by the last example:
25 \code lemon::ListGraph::Node \endcode
27 If the graph fits the ExtendableGraphComponent concept, then you can add new nodes
28 to the graph with the addNode() member function. It returns the newly added node
29 (as value). So if you need the new node to do something useful with it, for example
30 create a edge, assign a value to it through \ref map1 maps.
31 \code lemon::ListGraph::Node new_node = graph.addNode(); \endcode
33 If the graph fits the ErasableGraphComponent concept you also can remove nodes
34 from the graph with the erase() member function.
35 \code graph.erase( new_node ); \endcode
37 You don't have to store every node in a variable, you can access individual nodes
38 with node iterators discussed in the next section. But how do you know which
40 The graph class has the id( Node n ) member function providing an unique identifier
41 assigned to every node.
44 \subsection basic_edge Edges
45 An Edge is what you think it is. It goes from one node to another node (they can
46 be identical). If the graph class is directed, the Edge is directed too. Otherwise
47 the edge is considered undirected and called UEdge.
48 \code lemon::ListUGraph::UEdge \endcode
50 The addEdge() member function will create a new edge. It has two arguments, the
51 source node and the target node. The graph class must be extendable.
52 \code lemon::ListGraph::Edge new_edge = graph.addEdge( src_node, trg_node ); \endcode
53 You can handle edge similar as nodes. The erase() member function has an edge taking
56 You can ask for the source or target node of the edge by the corresponding member
59 graph.source( new_edge );
60 lemon::ListGraph::Node n = graph.target( new_edge ); \endcode
61 These functions are always legal even if the graph is undirected. UEdge has a
65 \section basic_iterators Iterators
66 Graphs are some kind of containers. And as you expect they have iterator types.
67 One fore nodes and a couple for edges - and special classes can have additional
68 iterators too. An example:
69 \code lemon::ListGraph::NodeIt \endcode
70 That is a node iterator. Every iterator type starts whit an name what refers to
71 the iterated object, and ends whit 'It'.
73 LEMON style iterators differs from \c stl or \c boost iterators in a very tasty
74 way. A graph has no begin or end - or at least a generic graph class has none.
75 If by some topology you could pick a good begin node, it would be misleading and
76 incorrect. A LEMON style iterator must be initialized at construction time.
77 The constructor takes the needed parameters - by a node iterator it's the graph
78 object. And will be compared to the lemon::INVALID to check if it's still valid.
79 Every iterator can be compared to INVALID. No \c begin() or \c end() needed.<br>
80 Let's see these things working together:
82 for( ListGraph::NodeIt n(graph); n != INVALID; ++n )
83 do_useful_things_whit_node(n);
85 Note that the function \c do_useful_things_with_node() expects a Node type argument
86 ad we just gave him the iterator. LEMON style iterators must provide "on demand
87 dereferencing". For example a NodeIt can be used everywhere a Node could. (In some
88 graph classes Node is the base class of NodeIt. But in other cases this is implemented
89 through typecast operator.)
91 <b>Very important!</b> The iteration has no defined order. There is absolutely no
92 guaranty that the next time the iteration will give us the nodes in the same order.
93 Don't use this order to identify nodes! Use the \c id() member function of the
94 graph class described above. (There is a powerful technique using maps right in
97 The \ref EdgeIt works exactly the same - nothing more to say. But there are \ref InEdgeIt
98 and \ref OutEdgeIt by directed graphs and \ref IncEdgeIt by undirected graphs.
99 They take two arguments. The first is a graph, the second is certain node of the
100 graph. InEdgeIt iterates on the incoming edges of that node and OutEdgeIt does it
101 on the outgoing edges. The IncEdgeIt of course iterates every edge connecting to
105 for( ListGraph::NodeIt n(graph); n != INVALID; ++n ) {
107 for( ListGraph::InEdgeIt e(graph,n); e != INVALID; ++e ) ++in;
108 for( ListGraph::OutEdgeIt e(graph,n); e != INVALID; ++e ) ++out;
110 std::cout << "#" << graph.id(n) << " node has " << in << " incoming and "
111 << out << "outgoing edges." << std::endl;
116 \section basic_ListGraph ListGraph - a versatile directed graph
117 As you see ListGraph satisfies most of the basic concepts and ideal for general
118 graph representations. It has an undirected version too: ListUGraph.