1 | /*! |
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2 | |
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3 | \page graphs Graphs |
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4 | |
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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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9 | The primary data structures of LEMON are the graph classes. They all |
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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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12 | as incoming and outgoing edges of a given node. This functionalities |
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13 | are defined in the \ref lemon::concept::Graph "Graph" concept. |
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14 | |
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15 | The next important graph type concept is the undirected graph concept |
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16 | what is defined in the \ref lemon::concept::UGraph "UGraph" concept class. |
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17 | Each undirected graphs provide node - undirected edge list interfaces. |
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18 | In addition the undirected graphs can be used as directed graphs so |
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19 | they are also conform to the \ref lemon::concept::Graph "Graph" concept. |
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20 | |
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21 | Usually the graphs can be sorted to two group, the first is the |
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22 | general topology graph types which can store any graph and the second |
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23 | are the special topology graphs like the \ref FullUGraph or the \ref |
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24 | GridUGraph. |
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25 | |
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26 | \li \ref lemon::ListGraph "ListGraph" is the most versatile graph class. It meets |
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27 | the \ref lemon::concept::ErasableGraph "ErasableGraph" concept |
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28 | and it also has some convenient extra features. |
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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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31 | price of this is that it only meets the |
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32 | \ref lemon::concept::ExtendableGraph "ExtendableGraph" concept, |
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33 | so you cannot delete individual edges or nodes. |
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34 | \li \ref lemon::FullGraph "FullGraph" |
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35 | implements a complete graph. It is a |
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36 | \ref lemon::concept::Graph "Graph", so you cannot |
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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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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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41 | |
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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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45 | the node set of another graph. The base graph can be an arbitrary graph and it |
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46 | is possible to attach several \ref lemon::EdgeSet "EdgeSet"'s to a base graph. |
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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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51 | The graph structures themselves can not store data attached |
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52 | to the edges and nodes. However they all provide |
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53 | \ref maps-page "map classes" |
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54 | to dynamically attach data the to graph components. |
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55 | |
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56 | The following program demonstrates the basic features of LEMON's graph |
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57 | structures. |
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58 | |
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59 | \code |
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60 | #include <iostream> |
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61 | #include <lemon/list_graph.h> |
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62 | |
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63 | using namespace lemon; |
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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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70 | ListGraph is one of LEMON's graph classes. It is based on linked lists, |
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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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86 | for (NodeIt i(g); i!=INVALID; ++i) |
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87 | for (NodeIt j(g); j!=INVALID; ++j) |
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88 | if (i != j) g.addEdge(i, j); |
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89 | \endcode |
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90 | |
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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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93 | |
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94 | \code |
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95 | std::cout << "Nodes:"; |
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96 | for (NodeIt i(g); i!=INVALID; ++i) |
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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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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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105 | \ref lemon::INVALID "INVALID". This is what we exploit in the stop condition. |
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106 | |
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107 | The previous code fragment prints out the following: |
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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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115 | for (EdgeIt i(g); i!=INVALID; ++i) |
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116 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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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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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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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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132 | for (OutEdgeIt i(g, first_node); i!=INVALID; ++i) |
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133 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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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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137 | for (InEdgeIt i(g, first_node); i!=INVALID; ++i) |
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138 | std::cout << " (" << g.id(g.source(i)) << "," << g.id(g.target(i)) << ")"; |
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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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153 | for (EdgeIt e(g); e!=INVALID; ++e) |
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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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157 | for (EdgeIt e(g); e!=INVALID; ++e) |
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158 | std::cout << g.id(e) << " (" << g.id(g.source(e)) << "," << g.id(g.target(e)) |
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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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172 | As we mentioned above, graphs are not containers rather |
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173 | incidence structures which are iterable in many ways. LEMON introduces |
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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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177 | In the example above we create an EdgeMap which assigns an integer value to all |
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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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182 | your own maps. You can read more about using maps \ref maps-page "here". |
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183 | |
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184 | */ |
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