This paper proposes an alternative way to identify nodes with high betweenness centrality. It introduces a new metric, k-path centrality, and a randomized algorithm for estimating it, and shows empirically that nodes with high k-path centrality have high node betweenness centrality. The randomized algorithm runs in time $O(κ^{3}n^{2-2α}\log n)$ and outputs, for each vertex v, an estimate of its k-path centrality up to additive error of $\pm n^{1/2+ α}$ with probability $1-1/n^2$. Experimental evaluations on real and synthetic social networks show improved accuracy in detecting high betweenness centrality nodes and significantly reduced execution time when compared with existing randomized algorithms.