Graph Local Overlap Measure: Adamic Adar Index

#Graph #Basics #Clustering

The Adamic Adar (AA) index is1

$$ \mathbf S_{\text{AA}}[v_1,v_2] = \sum_{u\in\mathcal N(u) \cap \mathcal N(v)} \frac{1}{\log d_u}, $$

where $d_u$ is the node degree of node $u$ and $\mathcal N(u)$ is the neighbor nodes of $u$.

If two nodes have shared neighbor, the degree of the neighbors will be at least 2. So it is safe to use $1/\log d_u$.


  1. Adamic2003 Adamic LA, Adar E. Friends and neighbors on the Web. Soc Networks. 2003;25: 211–230. doi:10.1016/S0378-8733(03)00009-1  ↩︎

Published: by ;

L Ma (2021). 'Graph Local Overlap Measure: Adamic Adar Index', Datumorphism, 09 April. Available at: https://datumorphism.leima.is/cards/graph/graph-local-overlap-adamic-adar-index/.

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  • cards/graph/graph-local-overlap-adamic-adar-index.md