The interdependence of hospitals is underappreciated in patient outcomes studies. We used a network science approach to foreground this interdependence. Specifically, within two large state-based interhospital networks, we examined the relationship of a hospital's network position with in-hospital mortality and length of stay. We constructed interhospital network graphs using data from the Healthcare Cost and Utilization Project and the American Hospital Association Annual Survey for Florida (2014) and California (2011). The exposure of interest was hospital centrality, defined as weighted degree (sum of all ties to a given hospital from other hospitals). The outcomes were in-hospital mortality and length of stay with sub-analyses for four acute medical conditions: pneumonia, heart failure, ischemic stroke, myocardial infarction. We compared outcomes for each quartile of hospital centrality relative to the most central quartile (Q4), independent of patient- and hospital-level characteristics, in this retrospective cross-sectional study. The inpatient cohorts had 1,246,169 patients in Florida and 1,415,728 in California. Compared to Florida's central hospitals which had an overall mortality 1.60%, peripheral hospitals had higher in-hospital mortality (1.97%, adjusted OR (95%CI): Q1 1.61 (1.37, 1.89), p<0.001). Hospitals in the middle quartiles had lower in-hospital mortality compared to central hospitals (%, adjusted OR (95% CI): Q2 1.39%, 0.79 (0.70, 0.89), p<0.001; Q3 1.33%, 0.78 (0.70, 0.87), p<0.001). Peripheral hospitals had longer lengths of stay (adjusted incidence rate ratio (95% CI): Q1 2.47 (2.44, 2.50), p<0.001). These findings were replicated in California, and in patients with heart failure and pneumonia in Florida. These results show a u-shaped distribution of outcomes based on hospital network centrality quartile. The position of hospitals within an inter-hospital network is associated with patient outcomes. Specifically, hospitals located in the peripheral or central positions may be most vulnerable to diminished quality outcomes due to the network. Results should be replicated with deeper clinical data.