Fully Dynamic Betweenness Centrality

@inproceedings{Pontecorvi2015FullyDB,
  title={Fully Dynamic Betweenness Centrality},
  author={Matteo Pontecorvi and Vijaya Ramachandran},
  booktitle={ISAAC},
  year={2015}
}
We present fully dynamic algorithms for maintaining betweenness centrality (BC) of vertices in a directed graph \(G=(V,E)\) with positive edge weights. BC is a widely used parameter in the analysis of large complex networks. We achieve an amortized \(O({\nu ^*}^2 \cdot \log ^3 n)\) time per update with our basic algorithm, and \(O({\nu ^*}^2 \cdot \log ^2 n)\) time with a more complex algorithm, where \(n = |V| \), and \({\nu ^*}\) bounds the number of distinct edges that lie on shortest paths… 
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References

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A Faster Algorithm for Fully Dynamic Betweenness Centrality
TLDR
This result improves on the amortized bound for fully dynamic BC in [Pontecorvi-Ramachandran2015] by a logarithmic factor and matches the fully dynamic APSP bound in Thorup for APSP in graphs with unique shortest paths.
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TLDR
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