Before revision:  In order to understand the origin of localization we track the spectra as a function of connection probability and directionality both. The kind of inhibitory and excitatory connections we are considering, low connection probability leads to localized eigenstates near boundary of the circular region, whereas large connection probabilities give rise to isolated delocalized eigenstates.
After revision:  In order to understand the origin of localization we track the spectra as a function of connection probability and directionality .