Degree and clustering coefficient (DCC) centrality
The
degree and clustering coefficient
(DCC) centrality quantifies node importance by combining information about a node’s degree and clustering coefficient with those of its neighbors [2]. The DCC centrality of node \(i\) is defined as
\begin{equation*}
c_{DCC}(i) = α I_d(i) + (1-α) I_c(i),
\end{equation*}
where the degree-based term
\begin{equation*}
I_d(i) = d_i + \sum_{j \in \mathcal{N}(i)} d_j
\end{equation*}
captures the contribution of node \(i\) and its immediate neighbors, and the clustering-based term
\begin{equation*}
I_c(i) = e^{-c_i} \sum_{j \in \mathcal{N}^{(2)}(i)} c_j
\end{equation*}
accounts for the clustering coefficient of node \(i\) and its second-hop neighbors. Here, \(d_i\) is the degree of node \(i\), \(c_i\) is its clustering coefficient, \(\mathcal{N}(i)\) is the set of immediate neighbors, and \(\mathcal{N}^{(2)}(i)\) denotes the set of neighbors exactly two hops away.
The parameter \(α \in [0,1]\) balances the relative importance of degree and clustering effects. Yang et al. [2] suggest determining \(α\) using an entropy-based approach:
\begin{equation*}
α = \frac{1 - E_1}{2 - E_1 - E_2},
\end{equation*}
where \(E_1\) and \(E_2\) are the entropies of the distributions of \(I_d(i)\) and \(I_c(i)\), respectively.
Nodes with high DCC centrality thus have a combination of high connectivity and tightly clustered neighborhoods, reflecting both local and semi-local structural influence.