Clustering degree algorithm (CDA)
The
clustering degree algorithm
(CDA) is designed to identify influential spreaders in weighted networks [2]. CDA combines the degree and strength of a node with the network topology and the differentiated contribution of its neighbors.
The CDA score of node \(i\), denoted \(c_{CDA}(i)\), is defined as
\[
c_{CDA}(i) = CD(i) + \sum_{j \in \mathcal{N}(i)} \frac{w_{ij}}{\max_{ij} w_{ij}} \, CD(j),
\]
where \(CD(i)\) is the clustering degree of node \(i\), given by
\[
CD(i) = \frac{α \sum_{j=1}^N a_{ij} + (1-α) \sum_{j=1}^N w_{ij}}{1 + \exp\Bigg[-\frac{\sum_{j,k} (w_{ij} + w_{ik}) a_{ij} a_{jk} a_{ki}}{2 (\sum_{j=1}^N w_{ij}) (\sum_{j=1}^N a_{ij} - 1)}\Bigg]},
\]
with \(α\) as a tunable parameter (set to 0.5).
For unweighted networks, \(CD\) is independent of \(α\), and the CDA score simplifies to
\[
c_{CDA}(i) = \frac{d_i}{1 + e^{-cl(i)}} + \sum_{j \in \mathcal{N}(i)} \frac{d_j}{1 + e^{-cl(j)}},
\]
where \(d_i\) and \(cl(i)\) denote the degree and clustering coefficient of node \(i\), respectively.