Hierarchical closeness

Summary

Hierarchical closeness (HC) is a structural centrality measure used in network theory or graph theory. It is extended from closeness centrality to rank how centrally located a node is in a directed network. While the original closeness centrality of a directed network considers the most important node to be that with the least total distance from all other nodes, hierarchical closeness evaluates the most important node as the one which reaches the most nodes by the shortest paths. The hierarchical closeness explicitly includes information about the range of other nodes that can be affected by the given node. In a directed network $G(V, A)$ where $V$ is the set of nodes and $A$ is the set of interactions, hierarchical closeness of a node $i$ ∈ $V$ called $C_{hc}(i)$ was proposed by Tran and Kwon as follows: