I made some minor mods. I would suggest that you enable strict; (you will have to do some work to get it so that it doesn't complain).
Update: Possible recoding below...

#!/usr/bin/perl -w
#use strict;  #### I would recommend you do this!!!

# Takes input in the form 'a,b|c'  
# How to run :  perl code.pl 'a,b|c' 'c,d|e' 'a,d|e'  
# Outputs a NX3 for the above input data.  
# Outputs connections in Nx2 form   
use Data::Dumper;  
  
print "@ARGV\n";

$arg=join(' ',@ARGV);   
@det=split //, $arg;  
  
for ($i=0; $i <=8; $i++)  
{$trip[$i]=$det[2*$i];}  
  
my @array;  
while (@trip) {  
  push(@array, [ splice(@trip, 0, 3) ]);  
}  
print "@$_\n" for @array;  
   
for ($i=0; $i <=2; $i++)  
 {  
   for ($j=0; $j <=1; $j++)  
   { $con[$i][$j]=$array[$i][$j];}  
  }   
  
print Dumper \@con;  #### use the Dumper!

print "\n==========connections======\n";  
print "from->to\n";   
print " @$_\n" for @con; 
 
my %HoA;  
foreach my $rowref (@con) {   #each @con is a ref to row
     ($key, $value) = @$rowref;  
     push @{$HoA{$key}}, $value;  
}
# PRINTING THE HASH 
foreach (keys %HoA) { 
print "$_ => @{$HoA{$_}}\n";  #was missing a curly pair
}
__END__
C:\TEMP>perl hasharray.pl "a,b|c" "c,d|e" "a,d|e"
a,b|c c,d|e a,d|e
a b c
c d e
a d e
$VAR1 = [
          [
            'a',
            'b'
          ],
          [
            'c',
            'd'
          ],
          [
            'a',
            'd'
          ]
        ];

==========connections======
from->to
 a b
 c d
 a d
c => d
a => b d
[download]

Update:

Maybe I'm missing something but this seems to be overly complex. Maybe this is all that is needed?

#!/usr/bin/perl -w
use strict;  

# Takes input in the form 'a,b|c'  
# How to run :  perl code.pl 'a,b|c' 'c,d|e' 'a,d|e'  
# Outputs a NX3 for the above input data.  
# Outputs connections in Nx2 form   
use Data::Dumper;  
  
print "Input args are: @ARGV\n";

my %hash;

foreach my $input (@ARGV)
{
   my($key, $value ) = ($input =~ m/\w/g)[0,1];
   #not sure what role if any the |c or |e plays in this?
   
   push @{$hash{$key}}, $value;
}

print Dumper \%hash;
__END__
C:\TEMP>perl hasharray2.pl "a,b|c" "c,d|e" "a,d|e"
Input args are: a,b|c c,d|e a,d|e
$VAR1 = {
          'c' => [
                   'd'
                 ],
          'a' => [
                   'b',
                   'd'
                 ]
        };
[download]

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