Recent studies have highlighted the role of gene networks in disease biology. To formally assess this, we constructed a broad set of pathway, network, and pathway+network annotations and applied stratified LD score regression to 42 diseases and complex traits (average N = 323K) to identify enriched annotations. First, we analyzed 18,119 biological pathways. We identified 156 pathway-trait pairs whose disease enrichment was statistically significant (FDR < 5%) after conditioning on all genes and 75 known functional annotations (from the baseline-LD model), a stringent step that greatly reduced the number of pathways detected; most significant pathway-trait pairs were previously unreported. Next, for each of four published gene networks, we constructed probabilistic annotations based on network connectivity. For each gene network, the network connectivity annotation was strongly significantly enriched. Surprisingly, the enrichments were fully explained by excess overlap between network annotations and regulatory annotations from the baseline-LD model, validating the informativeness of the baseline-LD model and emphasizing the importance of accounting for regulatory annotations in gene network analyses. Finally, for each of the 156 enriched pathway-trait pairs, for each of the four gene networks, we constructed pathway+network annotations by annotating genes with high network connectivity to the input pathway. For each gene network, these pathway+network annotations were strongly significantly enriched for the corresponding traits. Once again, the enrichments were largely explained by the baseline-LD model. In conclusion, gene network connectivity is highly informative for disease architectures, but the information in gene networks may be subsumed by regulatory annotations, emphasizing the importance of accounting for known annotations.