Genome-wide association studies (GWAS) have been widely used for understanding the associations of single-nucleotide polymorphisms (SNPs) with a disease. GWAS data are often combined with known biological networks, and they have been analyzed using graph-mining techniques toward a systems understanding of the biological changes caused by the SNPs. To determine which subgraphs are associated with the disease, a statistical test on each subgraph needs to be conducted. However, no statistically significant results were found because multiple testing correction causes an extremely small corrected significance level. We introduce a method called gLAMP to enumerate subgraphs having statistically significant associations with a diagnosis. gLAMP integrates the Limitless Arity Multiple-testing Procedure (LAMP) with a graph-mining algorithm called COmmon Itemset Network mining (COIN). LAMP gives us the smallest possible Bonferroni factor, and COIN provides us with efficient enumeration of testable subgraphs. Theoretical results of their combination show the potential to enumerate subgraphs statistically significantly associated with a disease.