  Developing effective coarse grained (CG) approach is a promising way for
studying dynamics on large size networks. In the present work, we have proposed
a strength-based CG (\sCG) method to study critical phenomena of the Potts
model on weighted complex networks. By merging nodes with close strength
together, the original network is reduced to a CG-network with much smaller
size, on which the CG-Hamiltonian can be well-defined. In particular, we make
error analysis and show that our strength-based CG approach satisfies the
condition of statistical consistency, which demands that the equilibrium
probability distribution of the CG-model matches that of the microscopic
counterpart. Extensive numerical simulations are performed on scale-free
networks, without or with strength-correlation, showing that this \sCG approach
works very well in reproducing the phase diagrams, fluctuations, and finite
size effects of the microscopic model, while the \dCG approach proposed in our
recent work [Phys. Rev. E 82, 011107(2010)] does not.
