Riverscape genetics, which applies concepts in landscape genetics to riverine ecosystems, lack appropriate quantitative methods that address the spatial autocorrelation structure of linear stream networks and account for bidirectional geneflow. To address these challenges, we present a general framework for the design and analysis of riverscape genetic studies. Our framework starts with the estimation of pairwise genetic distance at sample sites and the development of a spatially structured ecological network (SSEN) on which riverscape covariates are measured. We then introduce the novel bidirectional geneflow in riverscapes (BGR) model that uses principles of isolation-by-resistance to quantify the effects of environmental covariates on genetic connectivity, with spatial covariance defined using simultaneous autoregressive models on the SSEN and the generalized Wishart distribution to model pairwise distance matrices arising through a random walk model of geneflow. We highlight the utility of this framework in an analysis of riverscape genetics for brook trout (Salvelinus fontinalis) in north central Pennsylvania, USA. Using the fixation index (F_ST) as the measure of genetic distance, we estimated the effects of 12 riverscape covariates on geneflow by evaluating the relative support of eight competing BGR models. We then compared the performance of the top-ranked BGR model to results obtained from comparable analyses using multiple regression on distance matrices (MRM) and the program STRUCTURE. We found that the BGR model had more power to detect covariate effects, particularly for variables that were only partial barriers to geneflow and/or uncommon in the riverscape, making it more informative for assessing patterns of population connectivity and identifying threats to species conservation. This case study highlights the utility of our modeling framework over other quantitative methods in riverscape genetics, particularly the ability to rigorously test hypotheses about factors that influence geneflow and probabilistically estimate the effect of riverscape covariates, including stream flow direction. This framework is flexible across taxa and riverine networks, is easily executable, and provides intuitive results that can be used to investigate the likely outcomes of current and future management scenarios.