Common out-neighbor (CON) score
The
common out-neighbor (CON)
score quantifies node similarity by counting multiplicities based on the minimum number of interactions [2]. Let \(CON(i,j)\) denote the number of common out-neighbors shared by nodes \(i\) and \(j\), defined as
\begin{equation*}
CON(i,j) = \sum_{k=1}^{N} \min(a_{ik}, a_{jk})=\sum_{k=1}^{N} a_{ik}a_{jk} = |\mathcal{N}^{out}(i) \cap \mathcal{N}^{out}(j) |.
\end{equation*}
Then, the CON score of node \(i\), denoted by \(c_{CON}(i)\), is given by
\begin{equation*}
c_{CON}(i) = \sum_{j=1}^{N} CON(i,j) = \sum_{j=1}^{N} \sum_{k=1}^{N} a_{ik}a_{jk} = \sum_{k=1}^{N}a_{ik} \sum_{j=1}^{N} a_{jk} = \sum_{k \in \mathcal{N}^{out}(i)} d_k^{in}.
\end{equation*}
For undirected networks, the common out-neighbor (CON) score of node \(i\) reduces to the sum of the degrees of its neighbors.