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 $!;
}