  We present a detailed analysis of the Kitaev--Heisenberg model on a single
hexagon. The energy spectra and spin--spin correlations obtained using exact
diagonalisation indicate quantum phase transitions between antiferromagnetic
and anisotropic spin correlations when the Kitaev interactions increase. In
cluster mean-field approach frustrated nearest neighbor exchange stabilizes the
stripe phase in between the N\'eel phase and frustrated one which evolves
towards the Kitaev spin liquid.
