All cycle betweenness (ACC) centrality is a variation of betweenness centrality that accounts for all simple cycles passing through a node, rather than only shortest paths [2]. For node \(i\), the ACC centrality \(c_{ACC}(i)\) is defined as
\[
c_{ACC}(i) = \sum_{k=3}^{N} α^{\,k-2} \, s_k(i),
\]
where \(s_k(i)\) denotes the total number of simple cycles of length \(k\) that include node \(i\), and \(α \in (0,1)\) is an attenuation factor that downweights longer cycles.
To efficiently estimate \(s_k(i)\), Zhou et al. employ a belief propagation algorithm. In their experiments, they consider \(α = 0.1\) and \(α = 0.5\) to evaluate the influence of the attenuation factor on centrality values.

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] Zhou, X., Liang, X., Zhao, J., & Zhang, S. (2018). Cycle based network centrality. Scientific Reports, 8(1), 11749. doi: 10.1038/s41598-018-30249-4.