Volume centrality , also known as the Distributed Assessment of the Closeness Centrality Ranking (DACCER), is a semi-local centrality measure based on the degrees of nodes within an \(r\)-hop neighborhood [2]. The centrality score \(c_{V}(i)\) of a node \(i\) is defined as\[c_{V}(i) = \sum_{j \in \mathcal{N}^{(\leq r)}(i)} d_j,\]where \(\mathcal{N}^{(\leq r)}(i)\) denotes the set of nodes located within a topological distance \(r\) from node \(i\) (including \(i\) itself). Wehmuth and Ziviani [2] empirically demonstrated that volume centrality achieves good performance for \(r = 2\). This measure generalizes the sphere degree introduced by da F. Costa et al. [3], which corresponds to the special case of volume centrality with \(r = 2\). For \(r = 1\), Pei et al. [4] showed that volume centrality can outperform in-degree and PageRank centralities in certain empirical networks.

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] Wehmuth, K., & Ziviani, A. (2012). Distributed assessment of the closeness centrality ranking in complex networks. In Proceedings of the Fourth Annual Workshop on Simplifying Complex Networks for Practitioners (pp. 43-48). doi: 10.1145/2184356.2184368.
[3] del Rio, G., Koschützki, D., & Coello, G. (2009). How to identify essential genes from molecular networks?. BMC systems biology, 3(1), 102. doi: 10.1186/1752-0509-3-102.
[4] Pei, S., Muchnik, L., Andrade, Jr, J. S., Zheng, Z., & Makse, H. A. (2014). Searching for superspreaders of information in real-world social media. Scientific reports, 4(1), 5547. doi: 10.1038/srep05547.