Finding the contributions of transmission paths in statistical energy analysis (SEA) models has become an established valuable tool to detect and remedy vibro-acoustic problems. Paths are identified in SEA according to Craik's definition and recently, very efficient methods have been derived to rank them in the framework of graph theory. However, up to date classification schemes have only considered the mean values of loss factors for path comparison, their variance being ignored. This can result in significant errors in the final results. In this work it is proposed to address this problem by defining stochastic biparametric SEA graphs whose edges are assigned both, mean and variance values. Paths between subsystems are then compared according to a proposed cost function that accounts for the stochastic nature of loss factors. For an efficacious ranking of paths, the stochastic SEA graph is converted to an extended deterministic SEA graph where fast classification deterministic algorithms can be applied. The importance of nonneglecting the influence of the variance in path ranking is illustrated by means of some academic numerical examples.