Fig. 9: Summary of centrality metrics across nodes and edges.
From: A simulation framework for evaluating electronic order workflows in integrated health records
a Degree Centrality (Unweighted). b Betweenness Centrality (Weight: Duration/Count). c Closeness Centrality (Weight: Duration/Count). d Eigenvector Centrality (Weight: Count). e PageRank Centrality (Weight: Count). f Edge Betweenness Centrality. Degree, Betweenness, Closeness, Eigenvector, and PageRank centralities were computed to characterize each state’s structural importance. Formal definitions follow established formulations: Betweenness Centrality of node v as CB(v) = ∑s≠v≠tσst(v)/σst, where σst denotes the total number of shortest paths between nodes s and t, and σst(v) counts how many of those paths pass through node v. In weighted graphs, the shortest paths are computed based on cumulative edge weights. The Betweenness Centrality of an edge follows the same principle. PageRank Centrality is computed as \(PR(v)=\frac{1-d}{N}+d{\sum }_{u\in {\rm{In}}(v)}PR(u)/L(u)\), where d is a damping factor (commonly set to 0.85), N is the total number of nodes, In(v) represents the nodes linking to v, and L(u) is the out degree of node u.
