Mixed core, degree and entropy (MCDE) method
The
mixed core, degree, and entropy
(MCDE) method is a hybrid centrality measure that combines \(k\)-shell and degree centralities with a weighted entropy measure [2]. The entropy of node \(i\) is defined as
\begin{equation*}
H(i) = \sum_{k=0}^{k_{max}} p_k(i) \log_2 p_k(i),
\end{equation*}
where \(k_{\max}\) denotes the maximum \(k\)-shell index in the network and \(p_k(i)\) is the fraction of node \(i\)'s neighbors in the \(k\)th core,
\begin{equation*}
p_k(i) = \frac{|\{ j \in \mathcal{N}(i) : k_s(j) = k \}|}{d_i}.
\end{equation*}
The MCDE centrality of node \(i\) is then given by
\begin{equation*}
c_{MCDE}(i) = α k_s(i) + β d_i + γ H(i),
\end{equation*}
where \(d_i\) is the degree, \(k_s(i)\) is the \(k\)-shell score, and \(α, β, γ\) are weights controlling the contribution of each component. Sheikhahmadi and Nematbakhsh [2] suggest \(α = β = γ = 1\).
Three variations of MCDE have also been proposed:
- Mixed Core, Degree, and Weighted Entropy (MCDWE) : computes a weighted entropy \begin{equation*} H(i) = \sum_{k=0}^{k_{max}} \frac{p_k(i) \log_2 p_k(i)}{k_{max} - |\{r : \exists j \in \mathcal{N}(i), k_s(j) = r\}| + 1}. \end{equation*}
- Mixed Core, Semi-local Degree, and Entropy (MCSDE) : replaces degree \(k_i\) with LocalRank (semi-local) centrality.
- Mixed Core, Semi-local Degree, and Weighted Entropy (MCSDWE) : combines the MCDWE and MCSDE approaches.