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A penalty box approach for approximation betweenness and closeness centrality algorithms


Centrality metrics are used to find important nodes in social networks. In the days of ever-increasing social network sizes, it becomes more and more difficult to compute centrality scores of all nodes quickly. One of the ways to tackle this problem is to use approximation centrality algorithms using sampling techniques. Also, in situations where finding only high value individuals/important nodes is the primary objective, accuracy of rank ordering of nodes is especially important. We propose a new sampling method similar to Tabu search, called “penalty box approach,” which can be used for approximation closeness and betweenness algorithms. On a variety of graphs we experimentally demonstrate that this new method when combined with previously known methods, such as random sampling and linear scaling, produces better results. The evaluation is done based on two measures that assess quality of rank ordered lists of nodes when compared against the true lists based on their closeness and betweenness scores. Effects of graph characteristics on the parameters of the proposed method are also analyzed.

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This material is based in part on work supported by the Intelligence Advanced Research Projects Activity (IARPA) via Air Force Research Laboratory contract number FA8650-10-C-7062. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright annotation thereon.


The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, AFRL or the U.S. Government.

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Correspondence to Rakesh Nagi.



See Tables 1, 2, 3, 4.

Table 1 Comparison of sampling strategies for betweenness algorithm on various graph types based on Kendall-Tau distance
Table 2 Comparison of sampling strategies for closeness algorithm on various graph types based on Kendall-Tau distance
Table 3 Comparison of sampling strategies for betweenness algorithm on various graph types based on the number of Top-20 nodes
Table 4 Comparison of sampling strategies for closeness algorithm on various graph types based on the number of Top-20 nodes

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Khopkar, S.S., Nagi, R. & Tauer, G. A penalty box approach for approximation betweenness and closeness centrality algorithms. Soc. Netw. Anal. Min. 6, 4 (2016).

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  • Betweenness Centrality
  • Preferential Attachment
  • Linear Scaling
  • Closeness Centrality
  • Centrality Score