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

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 $1/\log d_u$.

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