I think abitkin wants to make sure that $b isn't in any of the lists in %edgeHash, not to make sure that this specific edge didn't already exist.

I think a better answer is:

next if $already_seen{$b}++;
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If the values are $b are densely packed small positive integers, an array may be a better choice of data structures for already_seen

The new code:

my %edgeHash;
my %countHash;
my %already_seen;
while(<stdin>){

    # Reading an edge list
    if(/^\s*([0-9]+)\s+([0-9]+)\S*$/){
        my $a = "$1";
        my $b = "$2";

        # Eliminate loops
        next if $already_seen{$b};

        push @{$edgeHash{$a}}, $b;
    }
}
[download]

I hope this helps.

Alan