network. Buyers and suppliers in the high corruption risk network have more interactions among themselves compared to other agencies and firms that are only in the low corruption risk network.<sup>21</sup>

**Table 7: Network statistics for the complete network and low/high corruption risk, Bulgaria, 2017–2019**

|Statistic|(1)<br>Complete network|(2)<br>Bottom<br>30th percentile|(3)<br>Top<br>30th percentile|
|---|---|---|---|
|CRI percentile value|—|0.20|0.52|
|Total contract value|BGN 20.74 billion|BGN 7.10 billion|BGN 4.86 billion|
|Nodes<br>Buyers<br>Suppliers|9,664<br>1,907 (20%)<br>7,754(80%)|3,684<br>848 (23%)<br>2,836(77%)|4,678<br>1,572 (34%)<br>3,106(66%)|
|Edges|19,263|5,267|5,964|
|Graph density|0.0004|0.0008|0.0005|
|Clusters|150|135|245|
|**Modularity**(stronger clustering of<br>buyer-supplier ties)|0.550|0.707|0.654|
|**Betweenness centrality**<sup>**a**</sup> (higher<br>values given to buyers/suppliers that<br>create shorter paths between two<br>nodes)|0.082|0.094|0.158|
|**Eigenvector centrality**<sup>**a**</sup>(higher values<br>given to buyers/suppliers that are<br>connected to buyers/suppliers with<br>more ties)|12.462|1.167|11.313|

_Note:_ a. These aggregated centrality measures are network measures based on the centrality scores of each node in the network. The higher the centrality scores, the more likely the nodes that are further apart interact through central agencies/firms.

To illustrate the different types of state capture patterns found in Bulgaria, we show in Figure 21 the three largest clusters found in 2017–2019. Cluster A is the largest cluster and although it is not fully captured, it demonstrates a high risk of state capture pattern where the high corruption risk ties dominate the center of the network with the lower corruption risk ties remaining on the periphery. Cluster B is the second largest and shows a partial state capture pattern as well. High corruption risk ties are found in the center, mixed with other low corruption risk ties.<sup>22</sup> Cluster C shows a network with several centers that are not captured and one captured center. This shows a pattern where high corruption risk procedures are not conducted in a systemic pattern throughout the network.

> 21 Each of the betweenness and eigenvector centralization metrics are commonly used network-level metrics stemming from the node-level centrality scores. The betweenness centralization attributes higher centrality scores to nodes that are connected to more edges. A node’s eigenvector centrality, on the other hand, considers the importance of neighboring nodes as well. In our case, the top 30 percent sample has a higher betweenness centralization of 0.158 compared to 0.094 for the bottom 30 percent subnetwork. Similarly, the top 30 percent sample also has higher eigenvector centralization of 11.313 compared to 1.167 for the bottom 30 percent subnetwork. This indicates that activity in the high corruption risk subnetwork is conducted in a more centralized pattern compared to the low corruption risk subnetwork.

> 22 It is also observed that the high corruption risk ties in cluster B have lower CRI scores than the corruption risk ties in cluster A.

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