Blood coagulation is a vital process for humans and other species. Following an injury to a blood vessel, a cascade of molecular signals is transmitted, inhibiting and activating more than a dozen coagulation factors and resulting in the formation of a fibrin clot that ceases the bleeding. In this process, Antithrombin (AT), encoded by the SERPINC1 gene is a key player regulating the clotting activity and ensuring that it stops at the right time. In this sense, mutations to this factor often result in thrombosis - the excessive coagulation that leads to the potentially fatal formation of blood clots that obstruct veins. Although this process is well known, it is still unclear why even single residue substitutions to AT lead to drastically different phenotypes. In this study, to understand the effect of mutations throughout the AT structure, we created a detailed network map of this protein, where each node is an amino acid, and two amino acids are connected if they are in close proximity in the three-dimensional structure. With this simple and intuitive representation and a machine learning framework trained using genetic information from more than 130 patients, we found that different types of thrombosis have emerging patterns that are readily identifiable. Together, these results demonstrate how clinical features, genetic data and in silico analysis are converging to enhance the diagnosis and treatment of coagulation disorders.