Graph Local Overlap Measure: Adamic Adar Index

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 $1/\log d_u$.