The decaying degree centrality (DDC) is a generalization of the classical degree centrality that accounts for the influence of all nodes in a network, with contributions decaying exponentially with distance [2]. For a node \(i \in \mathcal{N}\), the DDC score is defined as
\[
c_{DDC}(i) = \sum_{j=1}^N \frac{d_j}{N^{2 d_{ij}}},
\]
where \(d_j\) is the degree of node \(j\), \(d_{ij}\) is the shortest-path distance between nodes \(i\) and \(j\).
Nodes with high DDC values are not only well-connected themselves but are also close to other highly connected nodes, reflecting both local and quasi-global influence in the network. The axiomatic properties of DDC are analyzed in [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] Bandyopadhyay, S., Narayanam, R., & Murty, M. N. (2018). A generic axiomatic characterization for measuring influence in social networks. In 2018 24th international conference on pattern recognition (icpr) (pp. 2606-2611). IEEE. doi: 10.1109/ICPR.2018.8546109.