Few things:

• close your INPUT file.
• chomp your input.
• split the line.
• do some error checking on the input so you don't try to
  access what isn't there.

Like this:

#!/usr/bin/perl -w

  # Open our datafile
  open(INPUT, '< graduate.output.txt')
     or die "Couldn't open the file for reading\n";

  # build a data structure
  @url_info = <INPUT>;

  close(INPUT);

  while(1){
     print "Pick a number: ";
     chomp($index = <STDIN>);
     next if ($index >= scalar(@url_info));
     if($index =~ /^q/i){
        last;
     }
     @f = split(/,\s*/, $url_info[$index]);
     print "Link: $f[0]\n";
  }
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