Refining Approximating Betweenness Centrality Based on Samplings
  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 $1/\varepsilon$ using $\varepsilon t$ 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 proposes a non-adaptive BC approximation method with samplings on shortest paths. We investigate the possibility to give an adaptive algorithm with samplings on 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. 
Shiyu Ji, Zenghui Yan
cs.SI physics.soc-ph