Bayesian Networks are an established computational approach for data driven network inference. However, experimental data is limited in its availability and corrupted by noise. This leads to an unavoidable uncertainty about the correct network structure. Thus sampling or bootstrap based strategies are applied to obtain edge frequencies. In a more general sense edge frequencies can also result from integrating networks learned on different datasets or via different inference algorithms. Subsequently one typically wants to derive a biological interpretation from the results in terms of a consensus network. We here propose a log odds based edge score on the basis of the expected false positive rate and thus avoid the selection of a subjective edge frequency cutoff. Computing a score optimal consensus network in our new model amounts to solving the maximum weight acyclic subdigraph problem. We use a branch-and-cut algorithm based on integer linear programming for this task. Our empirical studies on simulated and real data demonstrate a consistently improved network reconstruction accuracy compared to two threshold based strategies.