We develop a three-step computing approach to explore a hierarchical ranking network for a society of captive rhesus macaques. The computed network is sufficiently informative to address the question: Is the ranking network for a rhesus macaque society more like a kingdom or a corporation? Our computations are based on a three-step approach. These steps are devised to deal with the tremendous challenges stemming from the transitivity of dominance as a necessary constraint on the ranking relations among all individual macaques, and the very high sampling heterogeneity in the behavioral conflict data. The first step simultaneously infers the ranking potentials among all network members, which requires accommodation of heterogeneous measurement error inherent in behavioral data. Our second step estimates the social rank for all individuals by minimizing the network-wide errors in the ranking potentials. The third step provides a way to compute confidence bounds for selected empirical features in the social ranking. We apply this approach to two sets of conflict data pertaining to two captive societies of adult rhesus macaques. The resultant ranking network for each society is found to be a sophisticated mixture of both a kingdom and a corporation. Also, for validation purposes, we reanalyze conflict data from twenty longhorn sheep and demonstrate that our three-step approach is capable of correctly computing a ranking network by eliminating all ranking error.