Mixed degree decomposition (MDD)
Mixed degree decomposition (MDD)
, also referred to as the \(m\)-shell method, is an extension of the classical \(k\)-shell method that introduces a tunable parameter \(λ\) to better rank the spreading ability of nodes in complex networks [2]. MDD decomposes the network based on both the residual and exhausted degrees of nodes.
The
residual degree
\(d_i^{(r)}\) of node \(i\) is defined as the number of links connecting it to nodes that remain in the network, while the
exhausted degree
\(d_i^{(e)}\) counts the links connecting node \(i\) to nodes that have already been removed. The
mixed degree
is then given by
\begin{equation*}
d_i^{(m)} = d_i^{(r)} + λ d_i^{(e)},
\end{equation*}
where \(λ \in [0,1]\) controls the relative contribution of exhausted links.
The MDD procedure performs a \(k\)-shell decomposition using \(d_i^{(m)}\) to iteratively remove nodes. In the limiting cases, when \(λ = 0\), the MDD score reduces to the standard \(k\)-shell centrality, and when \(λ = 1\), it is equivalent to the degree centrality. Zeng and Zhang [2] suggest using \(λ = 0.7\) for optimal performance.