[666] | 1 | /*! |
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| 2 | |
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[1638] | 3 | \page graphs Graphs |
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[666] | 4 | |
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[2111] | 5 | \todo Write a new Graphs page. I think it should be contain the Graph, |
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| 6 | UGraph and BpUGraph concept. It should be describe the iterators and |
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| 7 | the basic functions and the differences of the implementations. |
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| 8 | |
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[921] | 9 | The primary data structures of LEMON are the graph classes. They all |
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[756] | 10 | provide a node list - edge list interface, i.e. they have |
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| 11 | functionalities to list the nodes and the edges of the graph as well |
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[2116] | 12 | as incoming and outgoing edges of a given node. |
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[756] | 13 | |
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[2116] | 14 | Each graph should meet the \ref lemon::concept::Graph "Graph" concept. |
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| 15 | This concept does not make it possible to change the graph (i.e. it is |
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| 16 | not possible to add or delete edges or nodes). Most of the graph |
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| 17 | algorithms will run on these graphs. |
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[756] | 18 | |
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| 19 | |
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[2116] | 20 | In case of graphs meeting the full feature |
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| 21 | \ref lemon::concept::ErasableGraph "ErasableGraph" |
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| 22 | concept |
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| 23 | you can also erase individual edges and nodes in arbitrary order. |
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| 24 | |
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| 25 | The implemented graph structures are the following. |
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[921] | 26 | \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets |
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[959] | 27 | the \ref lemon::concept::ErasableGraph "ErasableGraph" concept |
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[1168] | 28 | and it also has some convenient extra features. |
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[921] | 29 | \li \ref lemon::SmartGraph "SmartGraph" is a more memory |
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| 30 | efficient version of \ref lemon::ListGraph "ListGraph". The |
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[1168] | 31 | price of this is that it only meets the |
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[959] | 32 | \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept, |
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[756] | 33 | so you cannot delete individual edges or nodes. |
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[921] | 34 | \li \ref lemon::FullGraph "FullGraph" |
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[1200] | 35 | implements a complete graph. It is a |
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[2111] | 36 | \ref lemon::concept::Graph "Graph", so you cannot |
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[756] | 37 | change the number of nodes once it is constructed. It is extremely memory |
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| 38 | efficient: it uses constant amount of memory independently from the number of |
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[1043] | 39 | the nodes of the graph. Of course, the size of the \ref maps-page "NodeMap"'s and |
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| 40 | \ref maps-page "EdgeMap"'s will depend on the number of nodes. |
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[756] | 41 | |
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[921] | 42 | \li \ref lemon::NodeSet "NodeSet" implements a graph with no edges. This class |
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| 43 | can be used as a base class of \ref lemon::EdgeSet "EdgeSet". |
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| 44 | \li \ref lemon::EdgeSet "EdgeSet" can be used to create a new graph on |
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[873] | 45 | the node set of another graph. The base graph can be an arbitrary graph and it |
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[921] | 46 | is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph. |
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[756] | 47 | |
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| 48 | \todo Don't we need SmartNodeSet and SmartEdgeSet? |
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| 49 | \todo Some cross-refs are wrong. |
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| 50 | |
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[1168] | 51 | The graph structures themselves can not store data attached |
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[756] | 52 | to the edges and nodes. However they all provide |
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[1043] | 53 | \ref maps-page "map classes" |
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[756] | 54 | to dynamically attach data the to graph components. |
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| 55 | |
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[921] | 56 | The following program demonstrates the basic features of LEMON's graph |
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[666] | 57 | structures. |
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| 58 | |
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| 59 | \code |
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| 60 | #include <iostream> |
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[921] | 61 | #include <lemon/list_graph.h> |
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[666] | 62 | |
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[921] | 63 | using namespace lemon; |
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[666] | 64 | |
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| 65 | int main() |
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| 66 | { |
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| 67 | typedef ListGraph Graph; |
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| 68 | \endcode |
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| 69 | |
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[921] | 70 | ListGraph is one of LEMON's graph classes. It is based on linked lists, |
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[666] | 71 | therefore iterating throuh its edges and nodes is fast. |
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| 72 | |
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| 73 | \code |
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| 74 | typedef Graph::Edge Edge; |
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| 75 | typedef Graph::InEdgeIt InEdgeIt; |
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| 76 | typedef Graph::OutEdgeIt OutEdgeIt; |
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| 77 | typedef Graph::EdgeIt EdgeIt; |
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| 78 | typedef Graph::Node Node; |
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| 79 | typedef Graph::NodeIt NodeIt; |
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| 80 | |
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| 81 | Graph g; |
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| 82 | |
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| 83 | for (int i = 0; i < 3; i++) |
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| 84 | g.addNode(); |
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| 85 | |
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[875] | 86 | for (NodeIt i(g); i!=INVALID; ++i) |
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| 87 | for (NodeIt j(g); j!=INVALID; ++j) |
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[666] | 88 | if (i != j) g.addEdge(i, j); |
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| 89 | \endcode |
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| 90 | |
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[1168] | 91 | After some convenient typedefs we create a graph and add three nodes to it. |
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| 92 | Then we add edges to it to form a complete graph. |
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[666] | 93 | |
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| 94 | \code |
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| 95 | std::cout << "Nodes:"; |
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[875] | 96 | for (NodeIt i(g); i!=INVALID; ++i) |
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[666] | 97 | std::cout << " " << g.id(i); |
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| 98 | std::cout << std::endl; |
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| 99 | \endcode |
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| 100 | |
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| 101 | Here we iterate through all nodes of the graph. We use a constructor of the |
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[875] | 102 | node iterator to initialize it to the first node. The operator++ is used to |
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| 103 | step to the next node. Using operator++ on the iterator pointing to the last |
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| 104 | node invalidates the iterator i.e. sets its value to |
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[921] | 105 | \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition. |
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[666] | 106 | |
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[875] | 107 | The previous code fragment prints out the following: |
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[666] | 108 | |
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| 109 | \code |
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| 110 | Nodes: 2 1 0 |
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| 111 | \endcode |
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| 112 | |
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| 113 | \code |
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| 114 | std::cout << "Edges:"; |
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[875] | 115 | for (EdgeIt i(g); i!=INVALID; ++i) |
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[986] | 116 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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[666] | 117 | std::cout << std::endl; |
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| 118 | \endcode |
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| 119 | |
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| 120 | \code |
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| 121 | Edges: (0,2) (1,2) (0,1) (2,1) (1,0) (2,0) |
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| 122 | \endcode |
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| 123 | |
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[1168] | 124 | We can also iterate through all edges of the graph very similarly. The |
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| 125 | \c target and |
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| 126 | \c source member functions can be used to access the endpoints of an edge. |
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[666] | 127 | |
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| 128 | \code |
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| 129 | NodeIt first_node(g); |
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| 130 | |
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| 131 | std::cout << "Out-edges of node " << g.id(first_node) << ":"; |
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[875] | 132 | for (OutEdgeIt i(g, first_node); i!=INVALID; ++i) |
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[986] | 133 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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[666] | 134 | std::cout << std::endl; |
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| 135 | |
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| 136 | std::cout << "In-edges of node " << g.id(first_node) << ":"; |
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[875] | 137 | for (InEdgeIt i(g, first_node); i!=INVALID; ++i) |
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[986] | 138 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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[666] | 139 | std::cout << std::endl; |
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| 140 | \endcode |
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| 141 | |
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| 142 | \code |
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| 143 | Out-edges of node 2: (2,0) (2,1) |
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| 144 | In-edges of node 2: (0,2) (1,2) |
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| 145 | \endcode |
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| 146 | |
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| 147 | We can also iterate through the in and out-edges of a node. In the above |
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| 148 | example we print out the in and out-edges of the first node of the graph. |
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| 149 | |
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| 150 | \code |
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| 151 | Graph::EdgeMap<int> m(g); |
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| 152 | |
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[875] | 153 | for (EdgeIt e(g); e!=INVALID; ++e) |
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[666] | 154 | m.set(e, 10 - g.id(e)); |
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| 155 | |
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| 156 | std::cout << "Id Edge Value" << std::endl; |
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[875] | 157 | for (EdgeIt e(g); e!=INVALID; ++e) |
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[986] | 158 | std::cout << g.id(e) << " (" << g.id(g.source(e)) << "," << g.id(g.target(e)) |
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[666] | 159 | << ") " << m[e] << std::endl; |
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| 160 | \endcode |
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| 161 | |
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| 162 | \code |
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| 163 | Id Edge Value |
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| 164 | 4 (0,2) 6 |
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| 165 | 2 (1,2) 8 |
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| 166 | 5 (0,1) 5 |
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| 167 | 0 (2,1) 10 |
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| 168 | 3 (1,0) 7 |
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| 169 | 1 (2,0) 9 |
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| 170 | \endcode |
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| 171 | |
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[873] | 172 | As we mentioned above, graphs are not containers rather |
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[921] | 173 | incidence structures which are iterable in many ways. LEMON introduces |
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[666] | 174 | concepts that allow us to attach containers to graphs. These containers are |
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| 175 | called maps. |
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| 176 | |
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[1168] | 177 | In the example above we create an EdgeMap which assigns an integer value to all |
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[666] | 178 | edges of the graph. We use the set member function of the map to write values |
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| 179 | into the map and the operator[] to retrieve them. |
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| 180 | |
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| 181 | Here we used the maps provided by the ListGraph class, but you can also write |
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[1043] | 182 | your own maps. You can read more about using maps \ref maps-page "here". |
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[666] | 183 | |
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| 184 | */ |
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