Gene co-expression networks provide a systems-level view of molecular alterations in diseases like cancer. While tumor and healthy tissues have been widely compared in network-based approaches, tumor-adjacent normal tissues (NAT) remain less explored, despite evidence of molecular alterations influenced by the tumor environment. Here, we constructed co-expression networks for tumor, NAT, and healthy tissues across four cancer types to investigate structural differences. Using uniformly processed transcriptomic data from TCGA and GTEx, we built weighted graphs and computed three centrality measures: weighted degree, betweenness, and clustering coefficient. Genes were classified into positive and negative classes based on prior disease association evidence. Statistical analyses showed significant differences in centrality distributions between networks and gene classes, particularly highlighting molecular distinctions in NAT samples. Functional enrichment of ranked gene lists further linked central genes to cancer-related pathways, and known driver genes displayed characteristic patterns across tissue types. Our findings support the observations that NAT samples are molecularly distinct from healthy tissues and reinforce the usefulness of centrality measures to capture structural signatures of cancer-related processes.