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%.