This approach builds on two following findings in cognitive science: (i) human cognition partially determines expressed behaviour and is directly linked to true personality traits; and (ii) in dyadic interactions individuals' nonverbal behaviours are influenced by their conversational partner behaviours. In this context, we hypothesise that during a dyadic interaction, a target subject's facial reactions are driven by two main factors, i.e. their internal (person-specific) cognitive process, and the externalised nonverbal behaviours of their conversational partner. Consequently, we propose to represent the target subjects (defined as the listener) person-specific cognition in the form of a person-specific CNN architecture that has unique architectural parameters and depth, which takes audio-visual non-verbal cues displayed by the conversational partner (defined as the speaker) as input, and is able to reproduce the target subject's facial reactions. Each person-specific CNN is explored by the Neural Architecture Search (NAS) and a novel adaptive loss function, which is then represented as a graph representation for recognising the target subject's true personality. Experimental results not only show that the produced graph representations are well associated with target subjects' personality traits in both human-human and human-machine interaction scenarios, and outperform the existing approaches with significant advantages, but also demonstrate that the proposed novel strategies such as adaptive loss, and the end-to-end vertices/edges feature learning, help the proposed approach in learning more reliable personality representations.