Modify your subs so the subname can be passed as an argument to sort e.g

sub by_num {
  my($x,$y) = ($a =~ /(\d+)/, $b =~ /(\d+)/);
  return $x <=> $y;
}
sub by_abc {
  return $a cmp $b;
}

my $f    = 'by_num';
my @args = qw/ foo1 bar2 baz3 /;

print "$f - ", sort($f @args), $/;

$f = 'by_abc';

print "$f - ", sort($f @args), $/;

__output__

by_num - foo1bar2baz3
by_abc - bar2baz3foo1
[download]

But your solution is fine as it stands (although you need to call the function in the sort block e.g sort { &$sort_network{$sortby} } keys %networks).
HTH

_________
broquaint