  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 real-world 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.
