Adamic–Adar index

The Adamic–Adar index is a measure introduced in 2003 by <a href="/facts/Lada_Adamic/SJhsN6p7">Lada Adamic</a> and Eytan Adar to predict links in a <a href="/facts/Social_network/kQg6aEVf">social network</a>, according to the amount of shared links between two nodes. It is defined as the sum of the inverse <a href="/facts/Logarithm/QeXaV97q">logarithmic</a> <a href="/facts/Degree_centrality/4n24KqLt">degree centrality</a> of the neighbours shared by the two nodes

 
 
 
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 {\displaystyle A(x,y)=\sum _{u\in N(x)\cap N(y)}{\frac {1}{\log {|N(u)|}}}}

where 
 
 
 
 N
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 {\displaystyle N(u)}
 
 is the <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of nodes adjacent to 
 
 
 
 u
 
 
 {\displaystyle u}
 
. The definition is based on the concept that common elements with very large neighbourhoods are less significant when predicting a connection between two nodes compared with elements shared between a small number of nodes.

Adamic–Adar index open-in-new

Adamic–Adar index