A measure of local uniqueness to identify linchpins in a social network with node attributes

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.

Keywords: centrality; network vulnerability; node attribute; patient-sharing networks.

Fig 1.

Diagram of the linchpin score, showing examples of a linchpin score measure of 0 (A), 1 (B), 0.5 (C), and 0.75 (D). Blue nodes have the same value for attribute c as node i.

Fig 2.

Illustration of the physician network. The color of nodes corresponds to their specialty and the size of the nodes corresponds to their linchpin score.

Fig 3.

Heatmap of the correlation matrix of linchpin, degree, betweenness, closeness, and eigenvector centrality for the physician network. Correlation was measured using Kendal’s Tau non-parametric correlation coefficient.

Fig. 4.

Mixed effect models predicting physician rurality with linchpin (A), closeness (B), degree (C), and betweenness (D) for each specialty. Odds Ratios (ORs) and 95% confidence intervals (CIs) are shown. The gray vertical line indicates OR = 1. ORs >1 indicate that rural physicians had higher values for a given network measure. The scales across the forest plots are not equal.