A variety of sequentially rejective, weighted Bonferroni type tests have been proposed, such as fi xed sequence procedures, tree structured and parallel gatekeeping tests, as well as fallback procedures. They allow to map the diff erence in importance as well as the relationship between various research questions onto an adequate multiple testing procedure. These procedures rely on the closed test principle and usually require the explicit speci fication of a large number of intersection hypothesis tests. We investigate the use of weighted directed graphs as a simple tool to visualize, construct and perform such Bonferroni type tests. There, each node corresponds to an elementary hypothesis, and the edges de fine a simple algorithm that sequentially tests each individual hypotheses. Furthermore, we propose adaptive multiple testing procedures defi ned by graphs, that allow to select promising hypotheses in an interim analysis and to restrict sampling of observations to the selected hypotheses.
