Discussion to: Bayesian graphical models for modern biological applications by Y. Ni, V. Baladandayuthapani, M. Vannucci and F.C. Stingo

It is a pleasure to congratulate Ni et al. (Stat Methods Appl 490:1–32, 2021) on the recent advances in Bayesian graphical models reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021). The authors have given considerable thought to the construction and estimation of Bayesian graphical models that capture salient features of biological networks. My discussion focuses on computational challenges and opportunities along with priors, pointing out limitations of the Markov random field priors reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021) and exploring possible generalizations that capture additional features of conditional independence graphs, such as hub structure and clustering. I conclude with a short discussion of the intersection of graphical models and random graph models.