We present preliminary results that quantify network robustness and fragility of Ewing sarcoma (ES), a rare pediatric bone cancer that often exhibits de novo or acquired drug resistance. By identifying novel proteins or pathways susceptible to drug targeting, this formalized approach promises to improve preclinical drug development and may lead to better treatment outcomes. Toward that end, our network modeling focused upon the IGF-1R-PI3K-Akt-mTOR pathway, which is of proven importance in ES. The clinical response and proteomic networks of drug-sensitive parental cell lines and their drug-resistant counterparts were assessed using two small molecule inhibitors for IGF-1R (OSI-906 and NVP-ADW-742) and an mTOR inhibitor (mTORi), MK8669, such that protein-to-protein expression networks could be generated for each group. For the first time, mathematical modeling proves that drug resistant ES samples exhibit higher degrees of overall network robustness (e.g., the ability of a system to withstand random perturbations to its network configuration) to that of their untreated or short-term (72-hour) treated samples. This was done by leveraging previous work, which suggests that Ricci curvature, a key geometric feature of a given network, is positively correlated to increased network robustness.