**Table 6: Network statistics for 2014–2016 and 2017–2019, Bulgaria**

|Statistic|(1)<br>(2014–2016)|(2)<br>(2017–2019)|
|---|---|---|
|Total contract value|BGN 17.02 billion|BGN 20.74 billion|
|Average CRI|0.36|0.40|
|Nodes<br>Buyers<br>Suppliers|13,885<br>2,815 (20%)<br>11,070(80%)|9,661<br>1,907 (20%)<br>7,754(80%)|
|Edges|28,764|19,263|
|Graph density|0.0003|0.0004|
|Clusters|284|150|
|**Modularity**(stronger clustering of buyer-supplier ties)|0.617|0.550|
|**Betweenness centrality**<sup>**a**</sup> (higher values given to<br>buyers/suppliers that create shorter paths between<br>two nodes)|0.111|0.082|
|**Eigenvector centrality**<sup>**a**</sup>(higher values given to<br>buyers/suppliers that are connected to<br>buyers/suppliers with more ties)|17.582|12.462|

_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 will interact through central agencies/firms.

To probe potential areas of state capture, we investigate the behavior of high- and low-risk portions of the buyer-supplier network separately and contrast them with each other. In line with the above theoretical model, we expect high-risk contracting relationships to be clustered if state capture is a widespread phenomenon in Bulgaria. We thus split the network into two subnetworks, representing the bottom 30 percent and top 30 percent of the average CRI of the contracting relationships. In addition, we use algorithms to detect buyer-supplier clusters that are characterized by a dense web of connections among them but by sparse connections with other buyer-supplier clusters.<sup>17</sup> We display the low and high corruption risk groups of buyers and suppliers separately in Figure 20. In these figures, the nodes are colored according to the identified clusters.<sup>18</sup> Clusters across both low- and high-risk portions of the contracting network are highlighted with the same color, that is, it is possible to see if the same network is present in the high- and/or low-risk parts of the network. In an imagined world, clusters would appear in only one of the subsamples (either bottom 30 percent or top 30 percent) which would indicate either complete state capture (if it only appears in the top 30 percent) or no state capture (if it appears in the bottom 30 percent sample).

The coloring of clusters reveals that most clusters contain low- as well as high-risk contracts, which suggests that there are few completely captured groups. Instead, the public procurement network in Bulgaria reveals different degrees of state capture among public agencies and the awarded firms. On the one end of the spectrum, we can identify, for example, the orange cluster on the top left of the

> 17 Specifically, we run the community detection algorithm in Gephi (Bastian, Heymann, and Jacomy 2009) which implements the modularity algorithm proposed by (Blondel et al. 2008) on the complete network. The algorithm identifies clusters based on organizations’ proximity to each other where the higher tie weights act as an attraction force to get nodes with similar edge weights and more interactions closer.

> 18 The identified communities are automatically assigned different colors to each node belonging to that community/cluster.

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