To examine the contribution of Non-Esterified Fatty-Acids (NEFA) and incretin to insulin-resistance and diabetes amelioration after malabsorptive metabolic-surgery that dramatically reduces circulating NEFA. In fact, NEFA infusion reduces glucose-stimulated insulin secretion and high-fat diets predict diabetes development. Six healthy-controls, 11 obese and 10 Type-2-Diabetic (T2D) subjects were studied before and 1 month after Bilio-Pancreatic Diversion (BPD). Twenty-four hours plasma glucose, NEFA, insulin, C-peptide, glucagon-like peptide-1 (GLP1) and gastric-inhibitory-polypeptide (GIP) time courses were obtained and analyzed by Granger causality and graph analyses. Insulin sensitivity and secretion were computed by the oral glucose minimal-model. Before metabolic-surgery NEFA had the strongest influence on the other variables in both obese and T2D subjects. After surgery, GLP1 and C-peptide controlled the system in obese and T2D subjects. Twenty-four hours GIP levels were markedly reduced after BPD. Finally, GLP1 played a central role, but also insulin and C-peptide had a comparable relevance in the network of healthy controls. After BPD insulin sensitivity was completely normalized in both obese and T2D individuals. Increased 24-hours GLP1 circulating levels positively influence glucose homeostasis in both obese and T2D subjects who underwent a malabsorptive bariatric operation. In these latter, the reduction of plasma GIP also contributed to the improvement of glucose metabolism. It is possible that the combination of a pharmaceutical treatment reducing GIP and increasing GLP1 plasma levels will contribute to a better glycemic control in T2D. The application of Granger causality and graph-analyses shed new light on the patho-physiology of metabolic surgery.