There are two steps to this. First you need to get a list of file names and sort them in the desired order. Then, open the files in a for loop over the sorted list.

my $path = '/path/to/dir';
my @names = glob $path . '/graph_set_*.out';

# @names is in alpha order, so sort numerically
my @sorted_names =
    sort {
        my ($x, $y);
        $a =~ /graph_set_(\d+)\.out$/ and $x = $1;
        $b =~ /graph_set_(\d+)\.out$/ and $y = $1;
        $x <=> $y
    } @names;
# That may benefit from a Schwartzian Transform

# Now, do the loop
for (@sorted_names) {
    open local(*IN), "< $_" or die $!;
    # ...
    close IN or die $!;
}
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If you can write for recent enough perl, three-arg open and lexical filehandles ('open my $fh, '<', $_ or die $!;') would be good. If you want all the handles open at the same time, push $fh onto an array or assign array elements to it.

After Compline,
Zaxo