It would be nice if you gave us some sample input data. Here is how I imagine a more complete example would work:

use strict;
use Graph::Undirected;
use Data::Dumper;

# Suppose list1 consists of the
# edges to add. Lowercase is first
# list, uppercase is second list.
# a to A, B, C
# b to C, D

my @list1 = (
   [ qw(a A) ],
   [ qw(a B) ],
   [ qw(a C) ],
   [ qw(b C) ],
   [ qw(b D) ]);

my $g = new Graph::Undirected;
foreach my $ids (@list1){
    $g->add_path(@$ids);
}
$Data::Dumper::Indent = 1;
print Data::Dumper->Dump([\$g], [qw(*g)]);
[download]

If I understand what you said you wanted to do, it would not make sense to have more than two items in each "add_path" call. That is, if you had [ qw(a A B C)] instead, there would be edges from a to A to B to C, which is wrong. You want a bipartite graph, correct?

Or perhaps you want something different. If you have an edge between every list2 vertex that shares an id, you would need not only A to B to C, but also C to A, a cycle. Please clarify your question with a more complete example.