Table 2 Social network analysis metrics that allow the identification of key players in wildlife trafficking networks

Degree centrality

The number of links directly connected to that player

Betweenness centrality

v _i is defined as follows. Consider the j ^th pair of players (v ^′ , v ^′′) _j for which v′ ̸= v _i and v′′ ̸= v _i . Let T _j be the number of shortest paths between v ^′ and v ^′′ . Let n _j be the number of these paths that contain player i. The betweenness centrality of v _i is \( {\displaystyle \sum_{j=1}^m\frac{n_j}{T_j}} \) where m is the number of player-pairs that connect by at least one path [35]. The measure incorporates by re-defining the length of a path between players v _i and v _j to be the sum of the link weight inverses across all of the links in the path [44]. A player with high betweenness centrality has control of information propagation in a network

Eigenvector centrality

Let W be the weighted-link adjacency matrix. Let e be the first eigenvector of W. The eigenvector centrality of player v _i is the i ^th component of e [35]. This metric measures a player’s influence by measuring how easily information can flow between a player and all other players regardless of the path taken [43]

Network connectedness

The largest eigenvalue of W. Let CI be this index

Gould-Fernandez total brokerage score

The GF total brokerage score for vi is the number of player pairs, v’, v” for which (v’, vi) and (vi, v”) are both in E but the link (v’, v’) is not in E [35]. A player with a high brokerage score functions as an intermediary (or broker) for many pairs of players not directly connected to each other