Finding k-highest betweenness centrality vertices in graphs

Lee, Min-Joong; Chung, Chin-Wan

doi:10.1145/2567948.2577358

Cited by 11 publications

(7 citation statements)

References 2 publications

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“…These algorithms usually keep track of the betweenness scores and additional information, such as the pairwise distances, and update them accordingly after a modification in the graph. Another problem that has recently been considered for betweenness and other centrality measures is the quick identification of the k most central nodes without computing the score of each node [6,34].…”

Section: Introductionmentioning

confidence: 99%

Improving the Betweenness Centrality of a Node by Adding Links

Bergamini

Crescenzi

D’Angelo

et al. 2018

ACM J. Exp. Algorithmics

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Betweenness is a well-known centrality measure that ranks the nodes according to their participation in the shortest paths of a network. In several scenarios, having a high betweenness can have a positive impact on the node itself. Hence, in this paper we consider the problem of determining how much a vertex can increase its centrality by creating a limited amount of new edges incident to it. In particular, we study the problem of maximizing the betweenness score of a given node -Maximum Betweenness Improvement (MBI) -and that of maximizing the ranking of a given node -Maximum Ranking Improvement (MRI). We show that MBI cannot be approximated in polynomial-time within a factor (1 − 1 2e ) and that MRI does not admit any polynomial-time constant factor approximation algorithm, both unless P = N P. We then propose a simple greedy approximation algorithm for MBI with an almost tight approximation ratio and we test its performance on several real-world networks. We experimentally show that our algorithm highly increases both the betweenness score and the ranking of a given node and that it outperforms several competitive baselines. To speed up the computation of our greedy algorithm, we also propose a new dynamic algorithm for updating the betweenness of one node after an edge insertion, which might be of independent interest. Using the dynamic algorithm, we are now able to compute an approximation of MBI on networks with up to 10 5 edges in most cases in a matter of seconds or a few minutes.

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Section: Introductionmentioning

confidence: 99%

Improving the Betweenness Centrality of a Node by Adding Links

Bergamini

Crescenzi

D’Angelo

et al. 2018

ACM J. Exp. Algorithmics

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show abstract

“…Future work includes extension to batch updates, where several edge updates occur at the same time, and to other centrality measures, such as betweenness. For the latter, a static algorithm for finding the top-k nodes with highest betweenness has been proposed in [15]. Thus, an interesting research question is whether this can be further improved and/or efficiently updated in dynamic networks.…”

Section: Discussionmentioning

confidence: 99%

Computing Top-k Closeness Centrality in Fully-dynamic Graphs

Bisenius¹,

Bergamini²,

Angriman³

et al. 2018

2018 Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX)

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Closeness is a widely-studied centrality measure. Since it requires all pairwise distances, computing closeness for all nodes is infeasible for large real-world networks. However, for many applications, it is only necessary to find the k most central nodes and not all closeness values. Prior work has shown that computing the top-k nodes with highest closeness can be done much faster than computing closeness for all nodes in real-world networks.However, for networks that evolve over time, no dynamic top-k closeness algorithm exists that improves on static recomputation. In this paper, we present several techniques that allow us to efficiently compute the k nodes with highest (harmonic) closeness after an edge insertion or an edge deletion. Our algorithms use information obtained during earlier computations to omit unnecessary work. However, they do not require asymptotically more memory than the static algorithms (i. e., linear in the number of nodes). We propose separate algorithms for complex networks (which exhibit the small-world property) and networks with large diameter such as street networks, and we compare them against static recomputation on a variety of real-world networks. On many instances, our dynamic algorithms are two orders of magnitude faster than recomputation; on some large graphs, we even reach average speedups between 10 3 and 10 4 .

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“…Thus, the approach is ineffective for applications where only a subset of the most central nodes is needed or when accuracy is needed. As this is indeed the case in many applications, several top-k centrality algorithms have been proposed recently for closeness [2] and betweenness [13]. Recently, a top-k algorithm for Katz centrality [17] was suggested.…”

Section: Introductionmentioning

confidence: 92%

Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

Grinten

Bergamini

Green

et al. 2018

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Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this paper, we consider the problem of computing rankings for Katz centrality.In particular, we propose upper and lower bounds on the Katz score of a given node. While previous approaches relied on numerical approximation or heuristics to compute Katz centrality rankings, we construct an algorithm that iteratively improves those upper and lower bounds until a correct Katz ranking is obtained. We extend our algorithm to dynamic graphs while maintaining its correctness guarantees. Experiments demonstrate that our static graph algorithm outperforms both numerical approaches and heuristics with speedups between 1.5× and 3.5×, depending on the desired quality guarantees. Our dynamic graph algorithm improves upon the static algorithm for update batches of less than 10000 edges. We provide efficient parallel CPU and GPU implementations of our algorithms that enable near real-time Katz centrality computation for graphs with hundreds of millions of nodes in fractions of seconds.

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Finding k-highest betweenness centrality vertices in graphs

Cited by 11 publications

References 2 publications

Improving the Betweenness Centrality of a Node by Adding Links

Improving the Betweenness Centrality of a Node by Adding Links

Computing Top-k Closeness Centrality in Fully-dynamic Graphs

Scalable Katz Ranking Computation in Large Static and Dynamic Graphs

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