  We investigate magnetic and charge correlations in graphene by using the
formulation of extended dynamical mean-field theory (E-DMFT) for two-sublattice
systems. First, we map the average non-local interaction onto the effective
static interaction between different sublattices, which is treated together
with the local interaction within an effective "two-orbital" local model. The
remaining part of the non-local interaction is considered by introducing an
effective retarded interaction within the E-DMFT approach. The non-local
susceptibilities in charge and spin channel are further evaluated in the ladder
approximation. We verify the applicability of the proposed method to describe
the effect of uniformly screened long-range Coulomb potential $\propto 1/r$, as
well as screened realistic long-range electron interaction [T. O. Wehling et
al., Phys. Rev. Lett. 106, 236805 (2011)] in graphene. We show that the
developed approach describes a competition of semimetal, spin density wave
(SDW), and charge-density-wave (CDW) correlations. The obtained phase diagram
is in a good agreement with recent results of functional renormalization group
(fRG) for finite large graphene nanoflakes and scaling analysis of quantum
Monte Carlo data on finite clusters. Similarly to the previously obtained
results within the fRG approach, the realistic screening of Coulomb interaction
by $\sigma$ bands causes moderate (strong) enhancement of critical long-range
interaction strength, needed for the SDW (CDW) instability, compared to the
results for the uniformly screened Coulomb potential.
