# A Visual Analytics Framework for Inter-Hospital Transfer Network of Stroke Patients
## 4 PatientFlow: The Visual Analytics Framework
### Comparative Cluster Topology Analysis  
Based on the task analysis results, we designed the cluster view with three types of visualizations for analyzing hub-and-spoke structures at the community level (T3). The node-link diagram at the top left uses a force-directed layout to depict the cluster's topology. We colored the node by degree centrality: red, orange, yellow, and blue correspond to values greater than 0.5, 0.4, 0.3, and 0, respectively (Figure 5). These values are determined heuristically during the meeting with the researchers. We classified a node with a degree centrality greater than 0.5 as a hub node and a node with a degree centrality less than 0.3 as a spoke node. Nodes with a centrality between 0.3 and 0.5 are assumed to be secondary hubs. We further divided the secondary hub range into two parts for detailed classification, using 0.4 as a threshold. As a result, one can distinguish a node receiving many patients from other hospitals within the cluster from a node receiving a relatively small number of patients while sending many patients to other hospitals. The chord diagram on the upper right (T5) enables a more detailed examination of patient transfer counts than the node-link diagram (Figure 5). While the node-link diagram provides a better topology overview, one can hardly compare the number of patients transferred between the hospitals. On the contrary, the thickness of the arcs in the chord diagram corresponds to the patient count, and one can visually compare them. Each circumference segment represents the hospital with a distinct background color. The arcs in the diagram have identical colors to the target hospital, and the sharp arrowhead represents the transfer direction. Thus, one could quickly identify the hospital with a considerable number of visited patients and the hospital receiving the most significant number of patients. The chord diagram can display stay patients with self-links, but since most patients stayed at the same hospital, it hindered analyzing transfer patterns. As a remedy to a relatively small number of transferred patients, we put a button at the title bar to toggle whether to include stay patients or not. The bar chart at the bottom shows the exact number of patients and follows the toggle state. Figure 4: Brushable bar charts for **(a)** the longest link within each cluster and **(b)** the degree centrality of each hospital. Darker gray background indicates the brushed area (i.e., selected range). The color strip on the right side of the degree centrality chart shows the value range for a primary hub (red), a secondary hub (orange and yellow), and a spoke hospital (blue). Then, we arranged additional space for the comparative analysis of clusters (T1). One can browse a list of clusters by scrolling but examining 90 clusters derived from 1009 hospitals could be challenging. After several reviews on network measures with medical researchers, we selected group degree centralization as a sorting criterion: one could start the analysis from the most/least centralized cluster. In addition, one can click the title bar on top of each cluster to select it, and the selected clusters move to the top of the list for future reference. The selected clusters also appear in the comparison view located at the bottom for comparison of network measures, enabling quantitative analysis of network topology. A user can select a measure from the list on the left (Figure 2e), and a bar chart shows the corresponding value of selected clusters. Moreover, one can select multiple measures to combine them into a normalized stacked bar chart (Section 5.1). It could aid the comparison of multiple proportions where their sum equals one (e.g., three types of transfer rates in Table 2). We aimed to encourage multi-perspective analysis by locating and analyzing a hospital of interest from another view (T1 and T2). Thus, we linked the charts within the cluster analysis area and the other charts from different perspectives.