  The Betweenness Centrality index is a very important centrality measure in
the analysis of a large number of networks. Despite its significance in a lot
of interdisciplinary applications, its computation is very expensive. The
fastest known algorithm presently is by Brandes which takes O(|V || E|) time
for computation. In real life scenarios, it happens very frequently that a
single vertex or a set of vertices is sequentially removed from a network. The
recomputation of Betweenness Centrality on removing a single vertex becomes
expensive when the Brandes algorithm is repeated. It is to be understood that
as the size of the network increases, Betweenness Centrality calculation
becomes more and more expensive and even a decrease in running time by a small
fraction results in a phenomenal decrease in the actual running time. The
algorithm introduced in this paper achieves the same in a significantly lesser
time than repetition of the Brandes algorithm. The algorithm can also be
extended to a general case.
