The VMM algorithm is a multi-attribute voting method for identifying key nodes in a network [2]. It is a variant of VoteRank, in which the voting ability \(v_i\) and voting score \(s_i\) of node \(i\) are defined as
\[
v_i = \frac{d_i}{(1+c_i) \, \max_j d_j},
\quad
s_i = d_i + \sqrt{d_i \sum_{j \in \mathcal{N}(i)} v_j},
\]
where \(d_i\) and \(c_i\) are the degree and clustering coefficient of node \(i\), respectively, and \(\mathcal{N}(i)\) denotes its set of neighbors.
At each iteration, the node \(k\) with the highest voting score \(s_k\) is selected as a key node. Once selected, the voting ability and voting score of node \(k\) are set to zero, and it no longer participates in subsequent voting rounds. The process repeats until the desired number of key nodes is identified.

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] Wang, G., Parthasarathy, R., & Li, Y. (2023). Key node identification voting method based on multi-attributes in social complex networks. In Proceedings of the 2023 3rd Guangdong-Hong Kong-Macao Greater Bay Area Artificial Intelligence and Big Data Forum (pp. 394-399). doi: 10.1145/3660395.3660462.