ClusterRank centrality
The
ClusterRank centrality
integrates both the degree information of a node and its neighbours, as well as the local clustering structure of the network [2]. The ClusterRank score of a node \(i\) is defined as
\begin{equation*}
c_{\text{ClusterRank}}(i) = f(c_i) \sum_{j \in \mathcal{N}(i)} \left( d_j^{out} + 1 \right),
\end{equation*}
where \(c_i\) denotes the clustering coefficient of node \(i\), \(\mathcal{N}(i)\) is the set of its neighbours (or followers), and \(d_j^{out}\) is the out-degree of node \(j\). The function \(f(c_i)\) accounts for the influence of \(i\)’s local clustering on its centrality and is commonly defined as \(f(c_i) = 10^{-c_i}\), which downweights nodes embedded in highly clustered regions. In this way, ClusterRank emphasizes nodes that connect different local clusters while still considering the importance of their neighbors.