Dithering and betweenness centrality in weighted graphs

Author(s):  
Santiago Segarra ◽  
Alejandro Ribeiro
2021 ◽  
Vol 182 (3) ◽  
pp. 219-242
Author(s):  
Mostafa Haghir Chehreghani ◽  
Albert Bifet ◽  
Talel Abdessalem

Graphs (networks) are an important tool to model data in different domains. Realworld graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r ∈ V (G), we propose an exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set ℛ𝒱(r), which is used to prune a huge amount of computations that do not contribute to the betweenness score of r. Time complexity of our algorithm depends on |ℛ𝒱(r)| and it is respectively Θ(|ℛ𝒱(r)| · |E(G)|) and Θ(|ℛ𝒱(r)| · |E(G)| + |ℛ𝒱(r)| · |V(G)| log |V(G)|) for unweighted graphs and weighted graphs with positive weights. |ℛ𝒱(r)| is bounded from above by |V(G)| – 1 and in most cases, it is a small constant. Then, for the cases where ℛ𝒱(r) is large, we present a simple randomized algorithm that samples from ℛ𝒱(r) and performs computations for only the sampled elements. We show that this algorithm provides an (ɛ, δ)-approximation to the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small.


2017 ◽  
Vol 17 (2) ◽  
pp. 169-182 ◽  
Author(s):  
Manuel Then ◽  
Stephan Günnemann ◽  
Alfons Kemper ◽  
Thomas Neumann

2022 ◽  
Vol 27 (2) ◽  
pp. 1-25
Author(s):  
Somesh Singh ◽  
Tejas Shah ◽  
Rupesh Nasre

Betweenness centrality (BC) is a popular centrality measure, based on shortest paths, used to quantify the importance of vertices in networks. It is used in a wide array of applications including social network analysis, community detection, clustering, biological network analysis, and several others. The state-of-the-art Brandes’ algorithm for computing BC has time complexities of and for unweighted and weighted graphs, respectively. Brandes’ algorithm has been successfully parallelized on multicore and manycore platforms. However, the computation of vertex BC continues to be time-consuming for large real-world graphs. Often, in practical applications, it suffices to identify the most important vertices in a network; that is, those having the highest BC values. Such applications demand only the top vertices in the network as per their BC values but do not demand their actual BC values. In such scenarios, not only is computing the BC of all the vertices unnecessary but also exact BC values need not be computed. In this work, we attempt to marry controlled approximations with parallelization to estimate the k -highest BC vertices faster, without having to compute the exact BC scores of the vertices. We present a host of techniques to determine the top- k vertices faster , with a small inaccuracy, by computing approximate BC scores of the vertices. Aiding our techniques is a novel vertex-renumbering scheme to make the graph layout more structured , which results in faster execution of parallel Brandes’ algorithm on GPU. Our experimental results, on a suite of real-world and synthetic graphs, show that our best performing technique computes the top- k vertices with an average speedup of 2.5× compared to the exact parallel Brandes’ algorithm on GPU, with an error of less than 6%. Our techniques also exhibit high precision and recall, both in excess of 94%.


2016 ◽  
Vol 51 (8) ◽  
pp. 1-13 ◽  
Author(s):  
Lei Wang ◽  
Fan Yang ◽  
Liangji Zhuang ◽  
Huimin Cui ◽  
Fang Lv ◽  
...  

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Silvia Zaoli ◽  
Piero Mazzarisi ◽  
Fabrizio Lillo

AbstractBetweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of $$\sim 20$$ ∼ 20 k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.


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