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Legged animals still outperform many terrestrial robots due to the complex interplay of various component subsystems. Centralization is a potential integrated design axis to help improve the performance of legged robots in variable terrain environments. Centralization arises from the coupling of multiple limbs and joints through mechanics or feedback control. Strong couplings contribute to a whole-body coordinated response (centralized) and weak couplings result in localized responses (decentralized). Rarely are both mechanical and neural couplings considered together in designing centralization. In this study, we use an empirical information theory-based approach to evaluate the emergent centralization of a hexapod robot. We independently vary the mechanical and neural coupling through adjustable joint stiffness and variable coupling of leg controllers, respectively. We found an increase in centralization as neural coupling increased. Changes in mechanical coupling did not significantly affect centralization during walking, but did change the total information processing of the neuromechanical control architecture. Information-based centralization increased with robotic performance in terms of cost of transport and speed, implying that this may be a useful metric in robotic design.