Social network analysis (SNA) has been widely used in physics education research (PER) in recent years, but mostly in a limited range of the available modalities. This paper describes a unique approach to egocentric, mixed-methods SNA applied to qualitative network data obtained from 100 interviews with women and/or queer professional physicists. We focus on our methods for obtaining quantitative network data from these qualitative sources and present novel techniques for the analysis of the networks. We also examine the ways in which egocentric and mixed-methods SNA techniques are aligned with critical methods and well suited to the study of difference, non-normativity, and experiences of marginalization in physics spaces and communities. We explore the limitations and potential applications of these methods and situate this work in the larger context of our study of these interviews. This work bridges a methodological gap between SNA and qualitative work on identity in PER and begins to develop our understanding of the way gender and sexual minority physicists experience support.