Social robots’ adaptation to individual needs, both physical and social, is crucial in a diverse society. Physical adaptability in human-robot interaction (HRI) has been well studied, but its social aspects are also becoming increasingly important. A key example is the handshake, exemplifying both physical interaction and social complexity. This study introduces a handshake robot with the Rowat-Selverston CPG controller, adjusting its response to human interactions. We estimate human individual differences from the internal state of the robot and analyze them together with the social attributes of the robot evaluated from the ROSAS index to determine the relationship between individual adaptation and social attributes. The results showed a correlation between the robot’s internal state (power, force, CPG conductance) and perceived social qualities (warmth, competence), with a small effect on handshake duration. This research highlights the relationship between a robot’s physical adaptability and social attributes, forming the basis for future robots that interact personally and socially, and is the foundation for research on advanced social adaptation mechanisms.