We report neutron scattering, magnetic susceptibility and Monte Carlo theoretical analysis to verify the short-range nature of the magnetic structure and spin-spin correlations in a Yb3Ga5O12 single crystal. The quantum spin state of Yb3+ in Yb3Ga5O12 is verified. The quantum spins organize into a short-ranged emergent director state for T<0.6 K derived from anisotropy and near-neighbor exchange. We derive the magnitude of the near-neighbor exchange interactions 0.6<J1<0.7K,J2=0.12 K and the magnitude of the dipolar exchange interaction, D, in the range 0.18<D<0.21 K. Certain aspects of the broad experimental dataset can be modeled using a J1D model with ferromagnetic near-neighbor spin-spin correlations while other aspects of the data can be accurately reproduced using a J1J2D model with antiferromagnetic near-neighbor spin-spin correlation. As such, although we do not quantify all the relevant exchange interactions, we nevertheless provide a strong basis for the understanding of the complex Hamiltonian required to fully describe the magnetic state of Yb3Ga5O12.