Physics graduate studies are substantial efforts on the part of individual students, departments, and institutions of higher education. Understanding the factors that lead to student success and attrition is crucial for improving these programs. One factor that has recently started to be investigated is the broadly defined students' experiences related to support structures. The Aspects of Student Experience Scale (ASES), a Likert-style survey, was developed by researchers to do just that. In this study, we leverage the network approach for Likert-style surveys (NALS) methodology to provide a unique interpretation of responses to the ASES instrument for well-defined demographic groups. We confirm the validity of our findings by studying the stability of the NALS themes and investigating how they are expressed within demographic-based networks. We find that for all four themes in the original ASES study, certain thematic trends capturing students' experiences vary across the demographic-based networks in meaningful ways. We also reveal that for some demographic groups, there is an interesting interplay between, and mixing of, the original themes. Finally, our study showcases how NALS can be applied to other Likert-style datasets.