An Efficient Estimation of a Node’s Betweenness

Agarwal, Manas; Singh, Rishi Ranjan; Chaudhary, Shubham; Iyengar, S. R. S.

doi:10.1007/978-3-319-16112-9_11

Cited by 7 publications

(6 citation statements)

References 20 publications

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“…1 3 , Lemma 3 guarantees that the probability of such failure is at most ε, if the number of samples…”

Section: E[ymentioning

confidence: 98%

“…To address the performance problem, people have turned to paralleled algorithms [19,5,22,23], randomized approximations [4,14,22,23,9,2,3], etc. It turns out that sampling plays an important role in these algorithms.…”

Section: Related Workmentioning

confidence: 99%

“…It turns out that sampling plays an important role in these algorithms. There are two categories on the state-of-art sampling approximation algorithms: uniform sampling (e.g., to sample nodes with identical probability) [4,14,24] and non-uniform sampling (e.g., each node has a different probability to be sampled) [22,23,9,2,3]. However, none of the existing methods can show dominating performance over the rest.…”

Section: Related Workmentioning

confidence: 99%

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Refining Approximating Betweenness Centrality Based on Samplings

Ji¹,

Yan²

2016

Preprint

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Betweenness Centrality (BC) is an important measure used widely in complex network analysis, such as social network, web page search, etc. Computing the exact BC values is highly time consuming. Currently the fastest exact BC determining algorithm is given by Brandes, taking O(nm) time for unweighted graphs and O(nm + n 2 log n) time for weighted graphs, where n is the number of vertices and m is the number of edges in the graph. Due to the extreme difficulty of reducing the time complexity of exact BC determining problem, many researchers have considered the possibility of any satisfactory BC approximation algorithms, especially those based on samplings. Bader et al. give the currently best BC approximation algorithm, with a high probability to successfully estimate the BC of one vertex within a factor of 1/ε using εt samples, where t is the ratio between n 2 and the BC value of the vertex. However, some of the algorithmic parameters in Bader's work are not yet tightly bounded, leaving some space to improve their algorithm. In this project, we revisit Bader's algorithm, give more tight bounds on the estimations, and improve the performance of the approximation algorithm, i.e., fewer samples and lower factors. On the other hand, Riondato et al proposes a non-adaptive BC approximation method with samplings on shortest paths. We investigate the possibility to give an adaptive algorithm with samplings on pairs of vertices. With rigorous reasoning, we show that this algorithm can also give bounded approximation factors and number of samplings. To evaluate our results, we also conduct extensive experiments using real-world datasets, and find that both our algorithms can achieve acceptable performance. We verify that our work can improve the current BC approximation algorithm with better parameters, i.e., higher successful probabilities, lower factors and fewer samples.

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“…1 3 , Lemma 3 guarantees that the probability of such failure is at most ε, if the number of samples…”

Section: E[ymentioning

confidence: 98%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Refining Approximating Betweenness Centrality Based on Samplings

Ji¹,

Yan²

2016

Preprint

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“…It is due to the time complexity for computing betweenness centrality [27]. Efficient algorithms for updating and estimating betweenness centrality measures in dynamic and large-size networks are discussed in [28][29][30].…”

Section: Formulationmentioning

confidence: 99%

Node-weighted centrality: a new way of centrality hybridization

Singh

Iyengar

2020

Comput Soc Netw

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Centrality measures have been proved to be a salient computational science tool for analyzing networks in the last two to three decades aiding many problems in the domain of computer science, economics, physics, and sociology. With increasing complexity and vividness in the network analysis problems, there is a need to modify the existing traditional centrality measures. Weighted centrality measures usually consider weights on the edges and assume the weights on the nodes to be uniform. One of the main reasons for this assumption is the hardness and challenges in mapping the nodes to their corresponding weights. In this paper, we propose a way to overcome this kind of limitation by hybridization of the traditional centrality measures. The hybridization is done by taking one of the centrality measures as a mapping function to generate weights on the nodes and then using the node weights in other centrality measures for better complex ranking.

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“…We compare our method with the available techniques in the literature and show that our method produces more efficient ordering than the currently known methods. $ This is an expanded and extended version of the results appeared in CompleNet 2015 [1].…”

mentioning

confidence: 93%

An efficient heuristic for betweenness estimation and ordering

Singh

Iyengar

Chaudhary

et al. 2018

Soc. Netw. Anal. Min.

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Centrality measures, erstwhile popular amongst the sociologists and psychologists, have seen broad and increasing applications across several disciplines of late. Amongst a plethora of application specific definitions available in the literature to rank the vertices, closeness centrality, betweenness centrality and eigenvector centrality (page-rank) have been the most important and widely applied ones. Networks where information, signal or commodities are flowing on the edges, surrounds us. Betweenness centrality comes as a handy tool to analyze such systems, but betweenness computation is a daunting task in large size networks. In this paper, we propose an efficient heuristic to determine the betweenness-ordering of k vertices (where k is very less than the total number of vertices) without computing their exact betweenness indices. The algorithm is based on a non-uniform node sampling model which is developed based on the analysis of Erdos-Renyi graphs. We apply our approach to find the betweenness-ordering of vertices in several synthetic and realworld graphs. The proposed heuristic results very efficient ordering even when runs for a linear time in the terms of the number of edges. We compare our method with the available techniques in the literature and show that our method produces more efficient ordering than the currently known methods. $ This is an expanded and extended version of the results appeared in CompleNet 2015 [1].

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An Efficient Estimation of a Node’s Betweenness

Cited by 7 publications

References 20 publications

Refining Approximating Betweenness Centrality Based on Samplings

Refining Approximating Betweenness Centrality Based on Samplings

Node-weighted centrality: a new way of centrality hybridization

An efficient heuristic for betweenness estimation and ordering

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