  In the presence of the charged impurities, we study the weak localization
(WL) effect by evaluating the quantum interference correction (QIC) to the
conductivity of Dirac fermions in graphene. With the inelastic scattering rate
due to electron-electron interactions obtained from our previous work, we
investigate the dependence of QIC on the carrier concentration, the
temperature, the magnetic field and the size of the sample. It is found that WL
is present in large size samples at finite carrier doping. Its strength becomes
weakened/quenched when the sample size is less than a few microns at low
temperatures as studied in the experiments. In the region close to zero doping,
the system may become delocalized. The minimum conductivity at low temperature
for experimental sample sizes is found to be close to the data.
