Here's a link to the on-line LEDA manual:

http://www.algorithmic-solutions.info/leda_manual/MANUAL.html

Here's a short list of some LEDA commands that may come in handy.

to see the graph LEDA has set up, use
    G.write(string s) - writes G to the file named s
Example: in Test 0 after the graph is set up the line
    G.write("g");
produces a file named g that looks exactly like this:

LEDA.GRAPH
void
void
4
|{}|
|{}|
|{}|
|{}|
6
1 2 0 |{}|
1 3 0 |{}|
2 3 0 |{}|
2 3 0 |{}|
4 2 0 |{}|
4 2 0 |{}|

skipping the first 3 lines, the file says there are 4 nodes, they do
not have a predeclared node label, there are 6 edges, which are listed,
again there is no predeclared edge label. notice that LEDA numbered the
nodes in the order they were created (as expected!).

if you insert the command
    H.write("h");
in the "check" routine (right before the call to is_bridgeless(H))
the file h will contain the graph that corresponds to the "in" array.
    if (alg=="carving") H.write("h");
will only print the graph that carving produced.
========================================================================
other useful LEDA commands

G.succ_node(v)- returns node after v
G.pred_node(v)- returns node before v
G.read(string s) - reads graph from s and assigns it to G

forall_adj_nodes(v,w)- nodes adjacent to w are successively assigned to v

=========================================================================
if you want to number the nodes from 0 to n-1 and refer to them by your
numbers, use 2 arrays:

  int n = G.number_of_nodes();

  node* node_ptr = new node[n]; //node_ptr[i] will point to the ith node
                                // i=0,...,n-1

  node_array<int> my_node_num (G);//my_node_number[v] will give v's number 

  node v=G.first_node();
  for ( int i=0; i<n; i++, v=G.succ_node(v) )
    {node_ptr[i]=v; my_node_num[v]=i;
    }

=========================================================================