Expression quantitative trait locus (eQTL) analysis associates SNPs with gene expression; these relationships can be represented as a bipartite network with association strength as "edge weights" between SNPs and genes. However, most eQTL networks use binary edge weights based on thresholded FDR estimates: definitions that influence reproducibility and downstream analyses. We constructed twenty-nine tissue-specific eQTL networks using GTEx data and evaluated a comprehensive set of network specifications based on false discovery rates, test statistics, and p values, focusing on the degree centrality-a metric of an SNP or gene node's potential network influence. We found a thresholded Benjamini-Hochberg q value weighted by the Z-statistic balances metric reproducibility and computational efficiency. Our estimated gene degrees positively correlate with gene degrees in gene regulatory networks, demonstrating that these networks are complementary in understanding regulation. Gene degrees also correlate with genetic diversity, and heritability analyses show that highly connected nodes are enriched for tissue-relevant traits.