# Fully Dynamic Betweenness Centrality

@inproceedings{Pontecorvi2015FullyDB,
title={Fully Dynamic Betweenness Centrality},
author={Matteo Pontecorvi and Vijaya Ramachandran},
booktitle={ISAAC},
year={2015}
}
• Published in ISAAC 9 December 2015
• Computer Science
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…
13 Citations
A Faster Algorithm for Fully Dynamic Betweenness Centrality
• Computer Science, Mathematics
ArXiv
• 2015
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.
Parallel Algorithm for Incremental Betweenness Centrality on Large Graphs
• Computer Science
IEEE Transactions on Parallel and Distributed Systems
• 2018
The serial implementation of the novel incremental algorithm, which decompose the graph into biconnected components and proves that processing can be localized within the affected components, is demonstrated to be up to 3.7 times faster than existing serial methods.
Temporal betweenness centrality in dynamic graphs
• Computer Science
International Journal of Data Science and Analytics
• 2019
The bi-objective notion of shortest–fastest path (SFP) in temporal graphs is proposed, which considers both space and time as a linear combination governed by a parameter, and a novel temporal betweenness centrality (TBC) metric is defined that outperforms static BC in the task of identifying the best vertices for propagating information.
• Computer Science
ACM J. Exp. Algorithmics
• 2018
This article considers the problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it and proposes a simple greedy approximation algorithm for MBI with an almost tight approximation ratio and test its performance on several real-world networks.
Hierarchical Decomposition for Betweenness Centrality Measure of Complex Networks
• Computer Science
Scientific reports
• 2017
This work proposes a new hierarchical decomposition approach to speed up the betweenness computation of complex networks, and features a parallel structure, which is very suitable for parallel computation.
ABRA: Approximating Betweenness Centrality in Static and Dynamic Graphs with Rademacher Averages
• Computer Science
KDD
• 2016
We present ABRA, a suite of algorithms to compute and maintain probabilistically-guaranteed, high-quality, approximations of the betweenness centrality of all nodes (or edges) on both static and
Algorithms and Frameworks for Graph Analytics at Scale
This thesis presents a linear-space parallel incremental algorithm for updating betweenness centrality in large evolving graphs, which is up to an order of magnitude faster than the state-of-the-art parallel incremental algorithms.
Bavarian: Betweenness Centrality Approximation with Variance-Aware Rademacher Averages
• Computer Science, Mathematics
KDD
• 2021
Bavarian, a collection of sampling-based algorithms for approximating the Betweenness Centrality of all vertices in a graph, is presented and it is proved that, for all estimators, the sample size sufficient to achieve a desired approximation guarantee depends on the vertex-diameter of the graph, an easy-to-bound characteristic quantity.
Centrality Measures: A Tool to Identify Key Actors in Social Networks
• R. Singh
• Computer Science
Principles of Social Networking
• 2021
This chapter summarizes some of the centrality measures that are extensively applied for mining social network data and discusses various directions of research related to these measures.
Recent Advances in Fully Dynamic Graph Algorithms
• Computer Science
ArXiv
• 2021
A quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.

## References

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A Faster Algorithm for Fully Dynamic Betweenness Centrality
• Computer Science, Mathematics
ArXiv
• 2015
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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For graphs with a constant number of shortest paths between any pair of vertices, the algorithm maintains APASP and BC scores in amortized time $$O(n^2 \cdot \log n)$$ under decremental updates, regardless of the number of edges in the graph.
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This paper presents a novel approximation algorithm for computing betweenness centrality of a given vertex, for both weighted and unweighted graphs, based on an adaptive sampling technique that significantly reduces the number of single-source shortest path computations for vertices with high centrality.
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We present an incremental algorithm that updates the betweenness centrality (BC) score of all vertices in a graph G when a new edge is added to G, or the weight of an existing edge is reduced. Our
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This work gives a novel algorithm that reduces computation for the insertion of an edge into the graph, the first algorithm for the computation of betweenness centrality in a streaming graph.
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This paper proposes the first truly scalable algorithm for online computation of betweenness centrality of both vertices and edges in an evolving graph where new edges are added and existing edges are removed and is carefully engineered with out-of-core techniques and tailored for modern parallel stream processing engines that run on clusters of shared-nothing commodity hardware.
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The experimental study shows that the algorithms proposed are the first to make in-memory computation of a betweenness ranking practical for million-edge semi-dynamic networks and the accuracy is even better than the theoretical guarantees in terms of absolutes errors and the rank of nodes is well preserved.
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This work proposes a method that efficiently reduces the search space by finding a candidate set of vertices whose betweenness centralities can be updated and computes their betweenness centeralities using candidate vertices only.
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New algorithms for betweenness are introduced in this paper and require O(n + m) space and run in O(nm) and O( nm + n2 log n) time on unweighted and weighted networks, respectively, where m is the number of links.