Ranking vertices for active module recovery problem

Selecting a connected subnetwork enriched in individually important vertices is an approach commonly used in many areas of bioinformatics, including analysis of gene expression data, mutations, metabolomic profiles and others. It can be formulated as a recovery of an active module from which an experimental signal is generated. Commonly, methods for solving this problem result in a single subnetwork that is considered to be a good candidate. However, it is usually useful to consider not one but multiple candidate modules at different significance threshold levels. Therefore, in this paper we suggest to consider a problem of finding a vertex ranking instead of finding a single module. We also propose two algorithms for solving this problem: one that we consider to be optimal but computationally expensive for real-world networks and one that works close to the optimal in practice and is also able to work with big networks.