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Issue No. 09 - Sept. (2015 vol. 27)
ISSN: 1041-4347
pp: 2494-2506
Nicolas Kourtellis , Yahoo Labs, Barcelona, Spain
Gianmarco De Francisci Morales , , Aalto University, Helsinki, Finland
Francesco Bonchi , Yahoo Labs, Barcelona, Spain
Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best known algorithm runs in $_$\mathcal {O}(nm)$_$ time. The problems of efficiency and scalability are exacerbated in a dynamic setting, where the input is an evolving graph seen edge by edge, and the goal is to keep the betweenness centrality up to date. In this paper, we propose 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. Our algorithm 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. Hence, it is amenable to real-world deployment. We experiment on graphs that are two orders of magnitude larger than previous studies. Our method is able to keep the betweenness centrality measures up-to-date online, i.e., the time to update the measures is smaller than the inter-arrival time between two consecutive updates.
Data structures, Time complexity, Time measurement, Communities, Heuristic algorithms, Bridges

N. Kourtellis, G. D. Morales and F. Bonchi, "Scalable Online Betweenness Centrality in Evolving Graphs," in IEEE Transactions on Knowledge & Data Engineering, vol. 27, no. 9, pp. 2494-2506, 2015.
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