In the first place you could have replaced push @vertices with $unique{ $edges[$i][$j] } = undef and then you don't have to mess with shoehorning @uniqv into a hash just to pull out the keys.

Abstracting out the edges and vertices, what I see is going on is, you have a list of lists, and you just want the elements that are unique across the whole thing.

I would do something like:

sub unique_elements {
    my ( %unique );
    # @_ could be large, so I don't want to put the list in memory, or
+ even put a list of indices into mem like you do with 0 .. $#_
    for ( my $i = 0; $i < @_; $i++ ) {
        # but the inner lists are a small fixed size, so even though t
+he sollution is generalized, the inner values I do just stick in a li
+st, which I use for a hash slice to autovivify the keys
        @unique{@{$_[$i]}} = undef; # black magic warning! the first e
+lement in the slice is assigned undef, and the rest are autovivfied
    }
    return sort keys %unique;
}
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