Hybrid median centrality (HMC)
The
hybrid median centrality
(HMC) identifies influential nodes by aggregating rankings from multiple existing centrality measures [2]. Let there be \(m\) rankings of nodes based on \(m\) different centrality measures. For example, Fei et al. [2] consider \(m = 3\) measures: degree, closeness and betweenness centralities.
The node rankings are organized in an \(N \times m\) multi-attribute decision-making matrix:
\[
R =
\begin{bmatrix}
r_{11} & r_{12} & r_{13} \\
r_{21} & r_{22} & r_{23} \\
\vdots & \vdots & \vdots \\
r_{N1} & r_{N2} & r_{N3}
\end{bmatrix},
\]
where \(r_{ij}\) denotes the ranking of node \(i\) with respect to the \(j\)-th centrality measure.
The hybrid median centrality \(c_{\mathrm{HMC}}(i)\) of node \(i\) is then defined as the median of its maximum and minimum rankings:
\[
c_{\mathrm{HMC}}(i) = \frac{\min_j r_{ij} + \max_j r_{ij}}{2}.
\]
The effectiveness of HMC is typically evaluated using the susceptible-infected (SI) propagation model on real-world networks, such as Email, US Air97, Karate Club, and Jazz Musicians.