Although a majority of 30-day readmissions of hip-fracture (HFx) patients in the elderly are caused by non-surgical complications, little is known about which specific combinations of comorbidities are associated with increased risk of readmission. We therefore used bipartite network analysis to explore the complex associations between 70 comorbidities (defined by hierarchal condition categories as critical in this population) and (a) cases consisting of all 2,316 HFx patients without hospital complications in the 2010 Medicare claims database who were re-admitted within 30 days of discharge, and (b) controls consisting of an equal number of matched HFx patients who were not readmitted for at least 90 days since discharge. A network-wide analysis revealed nine patient/comorbidity co-clusters, of which two had a significantly different proportion of cases compared to the rest of the data. A cluster-specific analysis of the most significant co-cluster revealed that a pair of comorbidities (Renal Failure and Diabetes with no Complications) within the co-cluster had significantly higher risk of 30-day readmission, whereas another pair of comorbidities (Renal Failure and Diabetes with Renal or Peripheral Circulatory Manifestations), despite having a relatively more serious comorbidity, did not confer a higher risk. This counter-intuitive result suggests that HFx patients with more serious comorbidities may have better follow-up that reduces the risk of 30-day readmission, whereas those with specific relatively less-serious comorbidities may have less stringent follow-up resulting in unanticipated incidents that precipitate readmission. These analyses reveal the strengths and limitations of bipartite networks for identifying hypotheses for complex phenomena related to readmissions, with the goal of improving follow-up care for patients with specific combinations of comorbidities.