Neighborhood connectivity
The
neighborhood connectivity
(also referred to as the
average neighborhood degree
) of a node \(i\), denoted as \(c_{NC}(i)\), is defined as the average degree of all its nearest neighbors [2]. Formally,
\begin{equation*}
c_{NC}(i) = \frac{\sum_{j \in \mathcal{N}(i)} |\mathcal{N}(j)|}{|\mathcal{N}(i)|} = \frac{\sum_{j \in \mathcal{N}(i)} d_j}{d_i},
\end{equation*}
where \(\mathcal{N}(i)\) represents the set of neighbors of node \(i\) and \(d_i\) is the degree of node \(i\). For isolated nodes (i.e., nodes with no neighbors), the neighborhood connectivity is defined to be zero.
For weighted networks, a corresponding generalization known as the weighted average nearest-neighbors degree was introduced by Barrat et al. [3].