Network Analysis of Hospital Centrality Measures

A network consists of nodes and directional links between nodes.^{17,21,24,29,30,31} In our networks, hospitals were considered nodes, and interhospital transfers were considered directional links between nodes, weighted by the number of transfers between the hospitals.^17,29,30,31 We constructed 5 separate networks: (1) all transfers, (2) ED to inpatient transfers only, (3) inpatient to inpatient transfers only, (4) all transfers involving at least 1 operation or procedure, and (5) all transfers not involving any operation or procedure. For each network, we defined 3 centrality variables for each hospital: in-degree centrality (the normalized number of links directed to a node), out-degree centrality (the normalized number of links directed from a node), and centrality ratio (in-degree centrality divided by out-degree centrality, in which higher values indicated more incoming transfers per outgoing transfer)^29,30,31,32 (Figure 1).

Centrality measures were normalized by the maximum possible number of links based on the number of nodes in the network. In-degree and out-degree centrality measures ranged from 0 to 1 and were scaled by multiplying by 10 000. Centrality measures were calculated based on standard methods used for network analysis.^30,31,32 Based on standard definitions, in-degree centrality was calculated as the summation of links directed to a node in a given network, normalized by the maximum number of such links. Out-degree centrality was calculated as the summation of links directed away from a node in a given network, normalized by the maximum number of such links. Centrality ratio was calculated as in-degree centrality divided by out-degree centrality.