Code with the variablename:

$authoridno="authorid";
                        Bug Here      And Here
                         |             |
                         V             V
my $nodedata=$read->find('//$authoridno');
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You're using single quotes, which in Perl mean "take this as exact literal" and, most importantly "do not interpolate variables". You want double quotes instead of single quotes, and if you are a belt-and-suspenders type, curly braces aren't a bad idea:

my $nodedata=$read->find("//${authoridno}");
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