A standard paradigm in computational biology is to use interaction networks to analyze high-throughput biological data. Two common approaches for leveraging interaction networks are: (1) network ranking, where one ranks vertices in the network according to both vertex scores and network topology; (2) altered subnetwork identification, where one identifies one or more subnetworks in an interaction network using both vertex scores and network topology. The dominant approach in network ranking is network propagation which smooths vertex scores over the network using a random walk or diffusion process, thus utilizing the global structure of the network. For altered subnetwork identification, existing algorithms either restrict solutions to subnetworks in subnetwork families with simple topological constraints, such as connected subnetworks, or utilize ad hoc heuristics that lack a rigorous statistical foundation. In this work, we unify the network propagation and altered subnetwork approaches. We derive a subnetwork family which we call the propagation family that approximates the subnetworks ranked highly by network propagation. We introduce NetMix2, a principled algorithm for identifying altered subnetworks from a wide range of subnetwork families, including the propagation family, thus combining the advantages of the network propagation and altered subnetwork approaches. We show that NetMix2 outperforms network propagation on data simulated using the propagation family. Furthermore, NetMix2 outperforms other methods at recovering known disease genes in pan-cancer somatic mutation data and in genome-wide association data from multiple human diseases. NetMix2 is publicly available at https://github.com/raphael-group/netmix2.