Light propagating through optical fiber arrays tends to localize in only a few center cores. The recent experiments in two-dimensional single-mode optical fiber arrays suggest that an interplay of deterministic and random linear and nonlinear effects might be responsible for this localization. We study this phenomenon, both analytically and numerically, in a hexagonal optical fiber array similar to that used in the experiments. Our analysis reveals that Anderson localization is evident in the linear and intermediate regimes, where a larger fraction of initial energy is returned to the center fiber due to the stochastic effects. For very high levels of input energy, the system is strongly nonlinear, with the randomness amplifying the Kerr localization.