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 playerpairs that connect by at least one path [35]. The measure incorporates by redefining 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 weightedlink 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

GouldFernandez 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
