  Generally, the threshold of percolation in complex networks depends on the
underlying structural characterization. However, what topological property
plays a predominant role is still unknown, despite the speculation of some
authors that degree distribution is a key ingredient. The purpose of this paper
is to show that power-law degree distribution itself is not sufficient to
characterize the threshold of bond percolation in scale-free networks. To
achieve this goal, we first propose a family of scale-free networks with the
same degree sequence and obtain by analytical or numerical means several
topological features of the networks. Then, by making use of the
renormalization group technique we determine the threshold of bond percolation
in our networks. We find an existence of non-zero thresholds and demonstrate
that these thresholds can be quite different, which implies that power-law
degree distribution does not suffice to characterize the percolation threshold
in scale-free networks.
