Many types of networks, such as co-expression or ChIP-seq-based gene-regulatory networks, provide useful information for biomedical studies. However, they are often too full of connections and difficult to interpret, forming "indecipherable hairballs". To address this issue, we propose that a Bayesian network can summarize the core relationships between gene expression activities. This network, which we call the LatentDAG, is substantially simpler than conventional co-expression network and ChIP-seq networks (by two orders of magnitude). It provides clearer clusters, without extraneous cross-cluster connections, and clear separators between modules. Moreover, one can find a number of clear examples showing how it bridges the connection between steps in the transcriptional regulatory network and other networks (e.g., RNA-binding protein). In conjunction with a graph neural network (GNN), the LatentDAG works better than other biological networks in a variety of tasks, including prediction of gene conservation and clustering genes. Code is available at https://github.com/gersteinlab/LatentDAG. Supplementary data are available at Bioinformatics online.