Abstract
The interpretation of efficiency centrality is extended including nodes for which this metric acquires negative values. It is demonstrated that it happens either for nodes that are in shortest paths in which the nodes are the terminal nodes or if there are alternate shortest paths with similar length. It is shown that duplication of a node in a network leads to increase of the global efficiency, yet the efficiency centrality of the duplicated node is reduced by a factor of ½ with each subsequent replication.
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