Prions are transmissible, propagating alternative states of proteins. Prions in budding yeast propagate heritable phenotypes and can function in large-scale gene regulation, or in some cases occur as diseases of yeast. Other 'prionogenic' proteins are likely prions that have been determined experimentally to form amyloid in vivo, and to have prion-like domains that are able to propagate heritable states. Furthermore, there are over 300 additional 'prion-like' yeast proteins that have similar amino-acid composition to prions (primarily a bias for asparagines and glutamines). Here, we examine the protein functional and interaction networks that involve prion, prionogenic and prion-like proteins. Set against a marked overall preference for N/Q-rich prion-like proteins not to interact with each other, we observe a significant tendency of prion/prionogenic proteins to interact with other, N/Q-rich prion-like proteins. This tendency is mostly due to a small number of networks involving the proteins NUP100p, LSM4p and PUB1p. In general, different data analyses of functional and interaction networks converge to indicate a strong linkage of prionogenic and prion-like proteins, to stress-granule assembly and related biological processes. These results further elucidate how prions may impact gene regulation, and reveal a broader horizon for the functional relevance of N/Q-rich prion-like domains.