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Generating-function approach for bond percolations in hierarchical networks
We study bond percolations on hierarchical scale-free networks with the open
bond probability of the shortcuts and that of the ordinary bonds
. The system has a critical phase in which the percolating probability
takes an intermediate value . Using generating function approach, we
calculate the fractal exponent of the root clusters to show that
varies continuously with in the critical phase. We confirm
numerically that the distribution of cluster size in the critical
phase obeys a power law , where satisfies the
scaling relation . In addition the critical exponent
of the order parameter varies as , from
at to infinity at
.Comment: 8 pages, 8 figure
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