Difference between revisions of "Closeness"

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(basic definition of closeness)
 
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'''Closeness''' is one of the most popular measures to quantify structural importance of nodes in a network.
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'''Closeness''' is a radial measure of centrality that favors actors who are connected with many others via short paths.
  
It is defined as the reciprocal of a node's total distance to all others.
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The raw closeness score of a node <math>v</math> is defined as the reciprocal of its total distance to those it can reach via directed paths,
  
Thus, in terms of closeness, a node is ranked according to its mean distance to all other nodes.
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<math>c_C(v)=\frac{\text{number of reachable nodes}}{\sum\limits_{\text{reachable nodes } t} d_G(v,t)}</math>
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where <math>d_G(v,t)</math> denotes the length of a shortest directed path from <math>v</math> to <math>t</math>.
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If a [[link strength]] has been selected, the length of an <math>(v,t)</math>-path is the sum of the corresponding attribute values of all links in the path.

Revision as of 18:11, 17 January 2011

Closeness is a radial measure of centrality that favors actors who are connected with many others via short paths.

The raw closeness score of a node is defined as the reciprocal of its total distance to those it can reach via directed paths,

where denotes the length of a shortest directed path from to . If a link strength has been selected, the length of an -path is the sum of the corresponding attribute values of all links in the path.