Abstract
Network centrality measures assign importance to influential or key nodes in a network based on the topological structure of the underlying adjacency matrix. In this work, we define the importance of a node in a network as being dependent on whether it is the only one of its kind among its neighbors’ ties. We introduce linchpin score, a measure of local uniqueness used to identify important nodes by assessing both network structure and a node attribute. We explore linchpin score by attribute type and examine relationships between linchpin score and other established network centrality measures (degree, betweenness, closeness, and eigenvector centrality). To assess the utility of this measure in a real-world application, we measured the linchpin score of physicians in patient-sharing networks to identify and characterize important physicians based on being locally unique for their specialty. We hypothesized that linchpin score would identify indispensable physicians who would not be easily replaced by another physician of their specialty type if they were to be removed from the network. We explored differences in rural and urban physicians by linchpin score compared with other network centrality measures in patient-sharing networks representing the 306 hospital referral regions in the United States. We show that linchpin score is uniquely able to make the distinction that rural specialists, but not rural general practitioners, are indispensable for rural patient care. Linchpin score reveals a novel aspect of network importance that can provide important insight into the vulnerability of health care provider networks. More broadly, applications of linchpin score may be relevant for the analysis of social networks where interdisciplinary collaboration is important.
Highlights
IntroductionOne of its prime applications is to identify important or influential nodes based on their structural position
Centrality is one of the most established concepts in social network analysis
Linchpin scores of physicians in a patient‐sharing network Networks of physicians are frequently assembled based on administrative data of patient encounters: two physicians are connected if they have encounters with common patients
Summary
One of its prime applications is to identify important or influential nodes based on their structural position. Centrality measures such as degree, betweenness, and closeness centrality were introduced by Freeman in the 1970s (Freeman 1977, 1978). Eigenvector centrality, another measure of influence, was introduced by Bonacich and identifies influential nodes based on the prominence of their direct ties (Bonacich 1972). Redefining local and global influence in networks with overlapping communities, new representations of centrality measures have been developed that are designed to identify influential nodes in overlapping modular networks (Ghalmane et al 2019a, b)
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