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)]);