Energy equilibration in light-harvesting antenna systems normally occurs before energy is transferred to a reaction center. The equilibration mechanism is a characteristic of the excitation energy transfer (EET) network of the antenna. Characterizing this network is crucial in understanding the first step of photosynthesis. We present our phenomenology-based analysis procedure and results in obtaining the excitonic energy levels, spectral linewidths, and transfer-rate matrix of Light-Harvesting Complex II directly from its 2D electronic spectra recorded at 77 K with waiting times between 100 fs to 100 ps. Due to the restriction of the models and complexity of the system, a unique EET network cannot be constructed. Nevertheless, a recurring pattern of energy transfer with very similar overall time scales between spectral components (excitons) is consistently obtained. The models identify a "bottleneck" state in the 664-668 nm region although with a relatively shorter lifetime (∼4-6 ps) of this state compared to previous studies. The model also determines three terminal exciton states at 675, 677-678, and 680-681 nm that are weakly coupled to each other. The excitation energy equilibration between the three termini is found to be independent of the initial excitation conditions, which is a crucial design for the light-harvesting complexes to ensure the energy flow under different light conditions and avoid excitation trapping. We proposed two EET schemes with tentative pigment assignments based on the interpretation of the modeling results together with previous structure-based calculations and spectroscopic observables.