Network science is an emerging tool in systems biology and oncology, providing novel, system-level insight into the development of cancer. The aim of this project was to study the signaling networks in the process of oncogenesis to explore the adaptive mechanisms taking part in the cancerous transformation of healthy cells. For this purpose, colon cancer proved to be an excellent candidate as the preliminary phase, and adenoma has a long evolution time. In our work, transcriptomic data have been collected from normal colon, colon adenoma, and colon cancer samples to calculating link (i.e., network edge) weights as approximative proxies for protein abundances, and link weights were included in the Human Cancer Signaling Network. Here we show that the adenoma phase clearly differs from the normal and cancer states in terms of a more scattered link weight distribution and enlarged network diameter. Modular analysis shows the rearrangement of the apoptosis- and the cell-cycle-related modules, whose pathway enrichment analysis supports the relevance of targeted therapy. Our work enriches the system-wide assessment of cancer development, showing specific changes for the adenoma state.