Background Techniques for reconstruction of biological networks which are based on perturbation experiments often predict direct interactions between nodes that do not exist. Transitive reduction removes such relations if they can be explained by an indirect path of influences. The existing algorithms for transitive reduction are sequential and might suffer from too long run times for large networks. They also exhibit the anomaly that some existing direct interactions are also removed. Results We develop efficient scalable parallel algorithms for transitive reduction on general purpose graphics processing units for both standard (unweighted) and weighted graphs. Edge weights are regarded as uncertainties of interactions. A direct interaction is removed only if there exists an indirect interaction path between the same nodes which is strictly more certain than the direct one. This is a refinement of the removal condition for the unweighted graphs and avoids to a great extent the erroneous elimination of direct edges. Conclusions Parallel implementations of these algorithms can achieve speed-ups of two orders of magnitude compared to their sequential counterparts. Our experiments show that: i) taking into account the edge weights improves the reconstruction quality compared to the unweighted case; ii) it is advantageous not to distinguish between positive and negative interactions since this lowers the complexity of the algorithms from NP-complete to polynomial without loss of quality.