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Statements

Subject Item
dbr:Closeness_centrality
dbo:wikiPageWikiLink
dbr:Hierarchical_closeness
Subject Item
dbr:Hierarchical_closeness
rdfs:label
Hierarchical closeness
rdfs:comment
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 where is the set of nodes and is the set of interactions, hierarchical closeness of a node ∈ called was proposed by Tran and Kwon as follows:
dcterms:subject
dbc:Network_theory dbc:Graph_theory dbc:Graph_algorithms dbc:Networks dbc:Network_analysis dbc:Algebraic_graph_theory
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43927242
dbo:wikiPageRevisionID
729496155
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dbr:Centrality dbc:Graph_algorithms dbr:Graph_theory dbc:Network_analysis dbc:Graph_theory dbc:Algebraic_graph_theory dbr:Network_theory dbc:Network_theory dbc:Networks
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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 where is the set of nodes and is the set of interactions, hierarchical closeness of a node ∈ called was proposed by Tran and Kwon as follows: where: * is the reachability of a node defined by a path from to , and * is the normalized form of original closeness (Sabidussi, 1966). It can use a variant definition of closeness as follows: where is the distance of the shortest path, if any, from to ; otherwise, is specified as an infinite value. In the formula, represents the number of nodes in that can be reachable from . It can also represent the hierarchical position of a node in a directed network. It notes that if , then because is . In cases where , the reachability is a dominant factor because but . In other words, the first term indicates the level of the global hierarchy and the second term presents the level of the local centrality.
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