Topological coefficient
The
topological coefficient
quantifies the extent to which a node shares its neighbors with other nodes in the network [2]. For a given node \(i\), the topological coefficient is defined as
\begin{equation*}
c_{\mathrm{top}}(i) = \frac{\sum_{j=1}^N |\mathcal{N}(i) \cap \mathcal{N}(j)|}{|\mathcal{N}(i)| \cdot |\{v: \mathcal{N}(i) \cap \mathcal{N}(v) \neq \emptyset\}|},
\end{equation*}
where \(\mathcal{N}(i)\) is the set of neighbors of \(i\).
The topological coefficient ranges from 0 to 1. A value of \(c_{\mathrm{top}}(i) = 0\) indicates that node \(i\) does not share any neighbors with other nodes,
while higher values indicate that a larger fraction of \(i\)'s neighbors are shared with other nodes. The coefficient equals 1 if and only if every neighbor of \(i\) is shared with every node that shares at least one neighbor with \(i\). Intuitively, nodes with a high topological coefficient are embedded in tightly interconnected neighborhoods, whereas nodes with low values are more topologically isolated.