that printed:
  A B C D E
A 0 1 0 0 0
B 1 0 1 0 0
C 0 1 0 1 1
D 0 0 1 0 0
E 0 0 1 0 0

##</code><code>##

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

=this prints
  A B C D
A 0 1 0 0
B 1 0 1 0
C 0 1 0 1
D 0 0 1 0
=cut

my @vars = qw(A B C D);
my @square_matrix = map{ my @x;
                         push (@x,0) foreach @vars;
                         [@x]
                       }@vars;
my $num =0;
my %ltr2num = map{ $_ => $num++ }@vars;

my @pairs = ("A B", "B C", "C D"); ### the user input ####

foreach my $pair (@pairs)
{
   my ($x, $y) = split ' ',$pair;
   enter_pair_in_matrix ( $ltr2num{$x},
                          $ltr2num{$y},
                          \@square_matrix
                         );
}

dump_square_matrix(\@vars,\@square_matrix);

sub enter_pair_in_matrix
{
   my ($x,$y,$ref_matrix) = @_;
   $ref_matrix->[$x][$y]= 1;
   $ref_matrix->[$y][$x]= 1;
}

sub dump_square_matrix
{
   my ($ref_vars, $ref_matrix) = @_;
   
   my @vars = @$ref_vars;
   print "  ","@vars\n";
   
   foreach (@$ref_matrix)
   {
      print shift @vars, " @$_\n";
   }
}