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while( my $file = <graph_set_*.out> ) {
    next unless $file =~ m[graph_set_[123]?[0-9].out];
...
    #Do stuff
    close IN;
}

for $file (sort{ $a=~/(\d+)/ <=> $b=~/(\d+)/ } <graph_set_*.out> ) {
    open...
    ....
    close...
}