4Genome-wide association studies (GWAS) have cataloged many sig-5 nificant associations between genetic variants and complex traits. How-6 ever, most of these findings have unclear biological significance, because 7 they often have small effects and occur in non-coding regions. Integra-8 2 / 29 networks are potentially informative to dissect the genetics of complex traits, 39 since, through cellular interactions, trait-associated variants are likely to be 40 topologically related 18 . Though promising, the full potential of regulatory 41 networks is yet to be unleashed in GWAS. For example, recent connectiv-42 ity analyses 15,19 identify enrichments of genetic signals across many traits 43 and networks, but do not leverage observed enrichments to further enhance 44 4 / 29 RSS-NET provides a unified framework (Fig. 1d-f) for two tasks: (1) test-78 ing whether a network is enriched for genetic associations; (2) identifying 79 which genes within this network drive the enrichment. To assess network 80 enrichment (Fig. 1g), RSS-NET computes a Bayes factor (BF) comparing the 81 "enrichment model" (M 1 : θ > 0 or σ 2 > 0) against the "baseline model" (M 0 : 82 θ = 0 and σ 2 = 0). To prioritize genes within enriched networks (Fig. 1h) RSS-83 NET contrasts posterior distributions of genetic effects (β) under M 0 and M 1 . 84 RSS-NET outputs results for these two tasks simultaneously. 85 RSS-NET improves upon its predecessor RSS-E 13 . Indeed RSS-NET in-86 cludes RSS-E as a special case where edge-enrichment σ 2 = 0 and only node-87 enrichment θ is learned from data. By estimating the additional parame-88 ter σ 2 , RSS-NET is more flexible than RSS-E, and thus, RSS-NET consis-89 tently outperforms RSS-E in various simulation scenarios, and often yields 90 better fit on real data. Despite different treatments of σ 2 , RSS-NET and 91 RSS-E share computation schemes (Supplementary Notes), which allows us 92 to build RSS-NET on the efficient algorithm of RSS-E. Software is available 93 at https://github.com/suwonglab/rss-net. 94 Method comparison based on simulations. The novelty of RSS-NET 95 lies in its use of regulatory network topology to infer enrichments from whole-96 genome association statistics, and more importantly, its automatic priori-97 tization of loci in light of inferred enrichments. We are not aware of any 98 published method with the same features. However, one could ignore topol-99 ogy and simply create SNP-level annotations based on proximity to network 100 nodes (Supplementary Notes). On the node-based annotations, there are meth-101 ods to test global enrichments or local associations using GWAS summary 102data. Here we use Pascal 21 , LDSC 10,22 and RSS-E 13 to benchmark RSS-NET 103 through genome-wide simulations on real genotypes 23 (Methods). 104 We started with simulations where RSS-NET modeling assumptions were 105 satisfied. Here we considered two genetic architectures: a sparse scenario 106 with most SNPs being null (β = 0), and, a polygenic scenario with most SNPs 107 being trait-associated...