DegreeDistance is a degree-based centrality measure designed to identify \(k\) influential nodes in a network [2]. The method proceeds iteratively as follows:


  1. Initialize the seed set \(S\) as empty. Select the node with the highest degree and add it to \(S\).

  2. Consider the next highest-degree node \(j\). If the distance \(d_{ij}\) between \(j\) and any node \(i \in S\) is less than a threshold \(d\), do not add \(j\) to the seed set. Otherwise, include \(j\) in \(S\).

  3. Repeat step 2 until \(|S| = k\).


Sheikhahmadi et al. [2] also proposed extensions to the DegreeDistance measure. Note that in networks with small diameter, the resulting seed set \(S\) may be significantly smaller than \(k\) due to the distance constraint.

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] Sheikhahmadi, A., Nematbakhsh, M. A., & Shokrollahi, A. (2015). Improving detection of influential nodes in complex networks. Physica A: Statistical Mechanics and its Applications, 436, 833-845. doi: 10.1016/j.physa.2015.04.035.