# A Visual Analytics Framework for Inter-Hospital Transfer Network of Stroke Patients
## 3 Analysis of Data and User Task
### Data Preprocessing  
In the visualization process, additional measures for the network are calculated. The calculated measures are mostly related to degree centrality and density, which were also used in a previous study [7]. However, while this study examined a nationwide network, the degree centrality of a hospital was not calculated for entire hospitals across the country. Instead, we first derive clusters through community detection, and then we measure the degree-centrality of a hospital within the belonging cluster. The community detection technique used in this study is the Louvain algorithm [12; 14; 24]. We used a variation of the algorithm [14] that reflects all characteristics of a directed (i.e., transfer direction) and weighted (i.e., the number of transferred patients) network. As a result, the measures for each node, each cluster, and the network are calculated (Table 2). The degree centrality of the \(i\)th node \((n_{i})\) in a cluster is the number of hospitals that sent patients to the node (i.e., in-degree) out of the total number of hospitals within the cluster, excluding the respective node \((g-1)\). Among three options (i.e., in-degree, out-degree, total degree) to calculate the degree centrality, the use of the in-degree in the calculation was determined after a review of network measures and confirmed by the collaborating  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Metric** & **Equation** & **Application** & \\ \hline \multirow{2}{*}{Node} & Degree centrality & \multirow{2}{*}{\(C_{D}(n_{i})=\frac{n^{n}}{g-1}\)} & \multirow{2}{*}{Find hub hospitals} & \multirow{2}{*}{(1) * [FOOTNOTE:*]Footnote *: \(n_{i}=\) ith node in a cluster, \(n_{i}^{n}=\) in-degree of node \(n_{i}\), \(n_{i}^{n}=\) out-degree of node \(n_{i}\); \({}^{\dagger}g=\) number of nodes in the cluster, \(C_{D}(n^{*})=\) largest value of \(C_{D}(n_{i})\) in the cluster, \(max\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]\) & Find highly & \\  & -centralization & \multirow{2}{*}{\(C_{\mathit{i}ntra}=\left\{ \begin{array}{l}\frac{\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]}{[(g-1)]} \\ 0,\;\;\;\;otherwise\end{array} \right.\)}} & \multirow{2}{*}{(2) [FOOTNOTE:*]Footnote *: \(n_{i}=\) ith node in a cluster, \(n_{i}^{n}=\) in-degree of node \(n_{i}\), \(n_{i}^{n}=\) out-degree of node \(n_{i}\); \({}^{\dagger}g=\) number of nodes in the cluster, \(C_{D}(n^{*})=\) largest value of \(C_{D}(n_{i})\) in the cluster, \(max\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]\) & \\  & -centralization & \multirow{2}{*}{\(K_{\mathit{i}ntra}=\left\{ \begin{array}{l}\frac{\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]} {[(g-1)]}\\ 0\;\;\;\;\;otherwise\end{array} \right.\)}} & \multirow{2}{*}{\(K_{\mathit{i}ntra}=\left\{ \begin{array}{l}\frac{\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]} \\ 0\;\;\;\;otherwise\end{array} \right.\)}} & \multirow{2}{*}{\(K_{\mathit{i}ntra}=\left\{ \begin{array}{l}\frac{\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]} \\ 0\;\;\;\;otherwise\end{array} \right.\)}} & \multirow{2}{*}{(3) [FOOTNOTE:*]Footnote *: \(n_{i}=\) ith node in a cluster, \(n_{i}^{n}=\) in-degree of node \(n_{i}\), \(n_{i}^{n}=\) out-degree of node \(n_{i}\); \({}^{\dagger}g=\) number of nodes in the cluster, \(C_{D}(n^{*})=\) largest value of \(C_{D}(n_{i})\) in the cluster, \(max\sum_{i=1}^{N}[C_{D}(n^{*})-C_{D}(n_{i})]\) & \\  & -centralization & \multirow{2}{*}{(2) [FOOTNOTE:*]Footnote *: \(n_{i}=\) ith node in a cluster, \(n_{i}^{n}=\) in-degree of node \(n_{i}\), \(n_{i}^{n}=\) out-degree of node \(n_{i}\); \({}^{\dagger}g=\) number of nodes in the cluster, \(Cmedical researchers who also participated in user task analysis (Section 3.4). They wanted to focus on the role of the hub hospital in receiving and treating patients from nearby spoke hospitals. We tested various thresholds of degree centrality to determine a hub hospital. In this study, heuristically, a node with a value of 0.5 or higher is classified as a hub node.