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Closeness centrality (or closeness) of a node is a measure of centrality in a network, calculated as the reciprocal of the sum of the length of the shortest paths between the node and all other nodes in the graph.
Thus, the more central a node is, the closer it is to all other nodes.
Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network.
It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.
Degree centrality is defined as the number of links incident upon a node (i.e., the number of ties that a node has).
The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network.
Note: connections above are not always unique (the same character can be encountered in different acts).
This is why the sum of the single act connections doesn't always result in the total number.
More details about speakers connections can be found here.