  We investigate site percolation in a hierarchical scale-free network known as
the Dorogovtsev- Goltsev-Mendes network. We use the generating function method
to show that the percolation threshold is 1, i.e., the system is not in the
percolating phase when the occupation probability is less than 1. The present
result is contrasted to bond percolation in the same network of which the
percolation threshold is zero. We also show that the percolation threshold of
intentional attacks is 1. Our results suggest that this hierarchical scale-free
network is very fragile against both random failure and intentional attacks.
Such a structural defect is common in many hierarchical network models.
