The EnRenew algorithm is a variant of the VoteRank algorithm that incorporates information entropy to evaluate node influence [2]. Initially, the seed set \(S\) is empty. Each node \(i\) votes for its neighbor \(j\) with a vote weight
\begin{equation*}
h_{ij} = -\frac{d_i}{\sum_{l \in \mathcal{N}(j)} d_l}
\log \left(\frac{d_i}{\sum_{l \in \mathcal{N}(j)} d_l} \right),
\end{equation*}
where \(d_i\) is the degree of node \(i\) and \(\mathcal{N}(j)\) denotes the neighbors of node \(j\).
The voting procedure iteratively executes the following steps:


  1. Each node \(i\) votes for its neighbors \(j\) using the weights \(h_{ij}\).

  2. Select the node \(k \notin S\) with the highest total votes \begin{equation*} s_k = \sum_{i=1}^{N} a_{ik} h_{ik} \end{equation*} and add it to the seed set \(S\).

  3. Update the voting weights \(h_{ij}\) for nodes within the \(l\)-hop neighborhood of node \(k\): \begin{equation*} h^{\mathrm{new}}_{ij} = \left( 1 - \frac{1}{2^{l-1} E_{\langle d \rangle}} \right) h_{ij}, \end{equation*} where \begin{equation*} E_{\langle d \rangle} = -\log \frac{1}{\langle d \rangle} \end{equation*} represents the information entropy of a node in a \(\langle d \rangle\)-regular graph, with \(\langle d \rangle\) being the average degree of the network. Guo et al. [2] suggest \(l = 2\).


References

[1] Shvydun, S. (2025). Zoo of Centralities: Encyclopedia of Node Metrics in Complex Networks. arXiv: 2511.05122 https://doi.org/10.48550/arXiv.2511.05122
[2] Guo, C., Yang, L., Chen, X., Chen, D., Gao, H., & Ma, J. (2020). Influential nodes identification in complex networks via information entropy. Entropy, 22(2), 242. doi: 10.3390/e22020242.