Table 3 Summary of the four reported connectivity measures from the PDNs. Degree, betweenness, closeness, and strength are defined for single diagnosis codes, while modularity is defined for the whole PDN based on a given clustering. For mathematical and formal definitions see [28] and [26]. Note that the C in the value range column stands for the total number of all diagnosis codes in the PDN
Network measure | Calculation | Value range | Interpretation |
|---|---|---|---|
Degree | Number of phi correlations shared with other diagnosis codes. | Min: 2 (or 0) Max: C – 1 | Simplest centrality measure that gives a general idea how involved a diagnosis code is with other diagnosis codes. Only the directly connected diagnosis codes are accounted for. *For the analyses in this study, all diagnosis codes with at most one significant phi-correlation were excluded, thus the minimum degree in PDN is 2, and not 0. |
Strength | Sum of the phi correlations shared with other diagnosis codes. | Min: 0 Max: C - 1 | Similar to degree but weighted with the phi correlations. A diagnosis code with a few very strong phi correlations and a diagnosis code with many weak phi correlations can have the same strength. Minimum value = There are no significant phi correlations. Maximum value = perfect phi correlation with all other diagnosis codes. |
Betweenness | The number of shortest paths between any two diagnosis codes of which this diagnosis code is a part of divided by all possible paths. The paths are weighted by the phi correlations. | Min: 0 Max: 1 | Most diagnosis codes have betweenness 0, since most diagnosis codes are not part of any shortest path [28]. This measure indicates how central one diagnosis code is relative to all other diagnosis codes. High betweenness may indicate that the diagnosis code mediates the correlation between other diagnosis codes, leads to many other diagnosis codes, or is the end point of many comorbidities. |
Closeness | The inverse of the total sum of the lengths of the shortest paths to all other diagnosis codes. The path lengths are weighted by the phi correlations. | Min: 0 Max: 1 | The less intermediary diagnosis codes there are between two diagnosis codes and the higher the phi correlations, the ‘closer’ the two diagnosis codes are. Closeness gives a measure of this for one diagnosis code averaged over all other diagnosis codes. High closeness of a given diagnosis code indicates that it is more central relative to the other diagnosis codes and may represent a clinically important aspect of the diseasome. Minimum value = no shortest paths lead through the diagnosis code. Maximum value = all shortest paths go through the diagnosis code and all shortest paths have length 1. |
Modularity | Number of phi correlations within a cluster divided by the number of all phi correlations minus the expected proportion of phi correlations within a random cluster. | Min: − 1 Max: 1 | Modularity can be used to compare different clustering methods or clustering of two networks with the same algorithm. Here used to sanity check the clustering from the Walktrap-algorithm. Modularity < 0: the clustering divides the PDN into subnetworks worse than expected by a random clustering. Modularity > 0: the clustering divides the PDN into subnetworks better than expected by a random clustering. |