You could modify your loop as follows:

foreach my $sequence (@bigram) {
    #my $count;   is this a bug?
    my @word = split ' ', $sequence;
    my $prev = shift @word;
    foreach $word (@word) {
        $count{"${prev}_${word}"}++;
        $prev = $word;
    }
}
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If "test.txt" contains:

a b n z
d f n z
v
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this prints:

n_z occurs 2 times
a_b occurs 1 times
d_f occurs 1 times
f_n occurs 1 times
b_n occurs 1 times
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Is this what you are looking for?

Note that my $count; seems to be a bug.

Update: Another solution would be to try to use List::MoreUtils qw(natatime);