Box 1.

Approaches to weighting and aggregating dyads in complex patient-sharing physician networks.

Problem	Approach
Weighting edges between physicians	Number of shared patients
	Volume of shared patient visits
	Volume of shared relative value units
Aggregating edges between hospitals	Sum of all physician dyads weights spanning pairs of hospitals
	Volume of unique patients with clinical encounters at each pair of hospitals
	Sum of physician dyads bridging pairs of hospitals

Note: Each approach for weighting and aggregating may be more or less appropriate depending upon the study design and research questions. In this work, edges between physicians were weighted by the volume of shared patient visits, and edges between hospitals were aggregated by summing the physician dyad weights spanning each pair of hospitals.