Before revision:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except some of eigenstates at boundary . As p_r is increased and network deviates from  community structure there is a sudden change in the localization property for  very small value of deformation from the perfect community structure.
After revision:  For a very well distinguished community structure (rewiring probability p_r \sim 0) , the whole spectra is localized except some of eigenstates at boundary of the circular distribution. As the network deviates from community structure there is a sudden change in the localization property for very small value of deformation from the perfect community structure.