I am trying to build a graph and to compute the max_flow using boost/graph/kolomogorov_max_flow.hpp.

That's quite an error message. I'm not entirely sure what's going wrong (besides the missing function call), but there are a couple of problems with your program.

First, you should not be using the old-style properties to define your graph. Use bundled properties. It's much cleaner and generates shorter error messages since it can avoid the recursive templates. See here: http://www.boost.org/doc/libs/1_36_0/libs/graph/doc/bundles.html. If you didn't find this in the documentation, don't worry. It's not very easy to find.

Second, you're trying to mix descriptors from two kinds of graphs (Traits and Graph). While this may compile some of the time, you shouldn't be doing it. If you're going to use bundled properties, you can set up your graph like this:

struct Node;
struct Arc;

typedef adjacency_list<vecS, vecS, directedS, Node, Arc> Graph;

struct Node {
  std::string name;

struct Arc {
  long capacity;
  long risidual;
  graph_traits<Graph>::edge_descriptor reverse;

You should probably choose better names for Node and Arc. See if these changes help you get rid of your errors.

Andrew Sutton