Graph.0.69 Module---how to get a DAG from graph with cycles

Here I use an example to illustrate the problem I met when using Graph
Theory Module: I have a directed graph looks like the following (see the
figure).
Edges in the original directed graph:
[main] -> [foo]; [main] -> [bar];
[foo] -> [trouble];
[trouble] -> [foo];

I want to find all the cycles in the graph. whenever I find a cycle, I
want to break it by deleting an edge starting from a vertex farthest
away from node [main] to get the following graph ---in this case,
deleting [trouble] -> [foo] because [trouble] is the farthest node in
this cycle.
So, edges after the desired manipulation are:
[main] -> [foo]; [main] -> [bar];
[foo] -> [trouble];
-----------------------fiugre of original graph------------
[main]
/ \
[foo] [bar]
/ /
/ /
[trouble]
-----------------------end of the figure-------------------

I tried to use @v = $g->connected_component_by_index($i), but it seems
to return single nodes (which is deemed as strongly connected component
itself), which is not what I want.
$g->find_a_cycle does not work either, because it returns same cycle no
matter how many times you call it.

I am newbie in perl. Can someone give me a suggestion how to utilize
the existing APIs in Graph.0.69 to achieve what I want?
Here is what I experimented a bit(which failed), and it may give a
better background of my question.

============================================================ ========
#mycode.pl
6
7 use Graph;
8 my $gcall = Graph->new;
11
12 while (<>) {
13 chomp;
14 if (/^(.*)\t->\t(.*)\t=>\w*\t->(\d*)/) {
15 $gcall->add_edge($1, $2);
16 print $1, " to ", $2, " with ", $3, "\n";
17 #print $2, "\n";
18 }
19
20 }
21########at this point, the graph has been built#############
46
47 foreach (1..5) {
48 print "SCC $_:",
$gcall->strongly_connected_component_by_index($_), "\n\n";
49 print "cycle $_:",
$gcall->find_a_cycle;
50}
######### my tries to try to report cycles, FAILED ####

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