How about Graph::Easy?

use Graph::Easy;
my $graph = Graph::Easy->new();
# I think I got all the edges added below?
$graph->add_edge(1,2);
$graph->add_edge(2,5);
$graph->add_edge(5,6);
$graph->add_edge(6,7);
$graph->add_edge(7,8);
$graph->add_edge(8,9);
$graph->add_edge(9,11);
$graph->add_edge(8,10);
$graph->add_edge(10,11);
$graph->add_edge(1,4);
$graph->add_edge(4,5);
$graph->add_edge(1,3);
$graph->add_edge(3,5);
$graph->add_edge(1,7);
print $graph->as_ascii;
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Output:

  +-----------------------------+
  |                             |
  |                             |
  |         +-------------------+-------------------+
  |         |                   v                   v
+---+     +---+     +---+     +---+     +---+     +---+     +---+     
++----+     +----+
| 4 | <-- |   | --> | 2 | --> | 5 | --> | 6 | --> | 7 | --> | 8 | --> 
+| 10 | --> | 11 |
+---+     |   |     +---+     +---+     +---+     +---+     +---+     
++----+     +----+
          |   |       ^         ^                             |       
+             ^
          | 1 | ------+         |                             |       
+             |
          |   |                 |                             v       
+             |
          |   |                 |                           +---+     
+             |
          |   |                 |                           | 9 | ----
+-------------+
          +---+                 |                           +---+
            |                   |
            |                   |
            v                   |
          +---+                 |
          | 3 | ----------------+
          +---+
[download]

UPDATE: Note Graph::Easy only *displays* graphs, it doesn't analyze them. To do graph analysis, you'll need Graph. Of course they use different object constructions, but fear not, Graph::Convert converts wonderfully between the two, so you can create, analyze and display graphs with these three modules (Graph, Graph::Easy, Graph::Convert) and they all depend on core modules - so no dependency spiral.