Human infants learn the names of objects and develop their own conceptual systems without explicit supervision. In this study, we propose methods for learning aligned vision-language conceptual systems inspired by infants' word learning mechanisms. The proposed model learns the associations of visual objects and words online and gradually constructs cross-modal relational graph networks. Additionally, we also propose an aligned cross-modal representation learning method that learns semantic representations of visual objects and words in a self-supervised manner based on the cross-modal relational graph networks. It allows entities of different modalities with conceptually the same meaning to have similar semantic representation vectors. We quantitatively and qualitatively evaluate our method, including object-to-word mapping and zero-shot learning tasks, showing that the proposed model significantly outperforms the baselines and that each conceptual system is topologically aligned.