of a <b> graph</b> (we will always mean a directed graph by that). 

 of a <b> graph</b> (we will always mean a directed graph by that and say

 <b> undirected graph </b> otherwise). 

 graphs then you might find it useful to use our library LEMON.

 graphs then you might find it useful to use our library LEMON. LEMON 

 defines various graph concepts depending on what you want to do with the 

 graph: a very good description can be found in the page

 about \ref graphs "graphs".

 You will also want to assign data to the edges or nodes of the graph, for example a length or capacity function defined on the edges. You can do this in LEMON using so called \ref maps "maps". You can define a map on the nodes or on the edges of the graph and the value of the map (the range of the function) can be practically almost any type. Read more about maps \ref maps-page "here".

 in that format (find the documentation of the format on the web). 

 in that format (find the documentation of the DIMECS file format on the web). 

 One can also store network (graph+capacity on the edges) instances and other things in DIMACS format: to see the details read the documentation of the \ref dimacs.h "Dimacs file format reader".

 One can also store network (graph+capacity on the edges) instances and other things in DIMACS format and use these in LEMON: to see the details read the documentation of the \ref dimacs.h "Dimacs file format reader".

 A simple program using the \ref lemon::Dijkstra "LEMON Dijkstra class" is

 The following code is a simple program using the \ref lemon::Dijkstra "LEMON

 as follows (we do not include the part that instantiates the graph and the length function):

 Dijkstra class" and it also shows how to define a map on the edges (the length

 function):

   typedef Graph::EdgeMap<int> LengthMap;

   Graph G;

     typedef ListGraph Graph;

   Node s, t;

     typedef Graph::Node Node;

   LengthMap cap(G);

     typedef Graph::Edge Edge;

 	...

     typedef Graph::EdgeMap<int> LengthMap;

   Dijkstra<Graph, LengthMap> 

 	dijkstra_test(G, cap);

     Graph g;

   dijkstra_test.run(s);

     //An example from Ahuja's book

     Node s=g.addNode();

     Node v2=g.addNode();

     Node v3=g.addNode();

     Node v4=g.addNode();

     Node v5=g.addNode();

     Node t=g.addNode();

     Edge s_v2=g.addEdge(s, v2);

     Edge s_v3=g.addEdge(s, v3);

     Edge v2_v4=g.addEdge(v2, v4);

     Edge v2_v5=g.addEdge(v2, v5);

     Edge v3_v5=g.addEdge(v3, v5);

     Edge v4_t=g.addEdge(v4, t);

     Edge v5_t=g.addEdge(v5, t);

     LengthMap len(g);

     len.set(s_v2, 10);

     len.set(s_v3, 10);

     len.set(v2_v4, 5);

     len.set(v2_v5, 8);

     len.set(v3_v5, 5);

     len.set(v4_t, 8);

     len.set(v5_t, 8);

     std::cout << "The id of s is " << g.id(s)<< ", the id of t is " << g.id(t)<<"."<<std::endl;

     std::cout << "Dijkstra algorithm test..." << std::endl;

     Dijkstra<Graph, LengthMap> dijkstra_test(g,len);

     dijkstra_test.run(s);

     std::cout << "The distance of node t from node s: " << dijkstra_test.dist(t)<<std::endl;

     std::cout << "The shortest path from s to t goes through the following nodes (the first one is t, the last one is s): "<<std::endl;

     for (Node v=t;v != s; v=dijkstra_test.predNode(v)){

 	std::cout << g.id(v) << "<-";

     }

     std::cout << g.id(s) << std::endl;