Adaptive algorithms for estimating betweenness and k-path centralities

Betweenness centrality and k-path centrality are two important indices that are widely used to analyze social, technological and information networks. In the current paper, first given a directed network G and a vertex r ∈ V(G), we present a novel adaptive algorithm for estimating betweenness score of r. Our algorithm first computes two subsets of the vertex set of G, called RF (r) and RT (r). They define the sample spaces of the start-points and the end-points of the samples. Then, it adaptively samples from RF (r) and RT (r) and stops as soon as some condition is satisfied. The stopping condition depends on the samples met so far, |RF (r)| and |RT (r)|. We show that compared to the well-known existing algorithms, our algorithm gives a better (λ, δ)-approximation. Then, we propose a novel algorithm for estimating k-path centrality of r. Our algorithm is based on computing two sets RF (r) and D(r). While RF (r) defines the sample space of the source vertices of the sampled paths, D(r) defines the sample space of the other vertices of the paths. We show that in order to give a (λ, δ)-approximation of the k-path score of r, our algorithm requires considerably less samples. Moreover, it processes each sample faster and with less memory. Finally, we empirically evaluate our proposed algorithms and show their superior performance. Also, we show that they can be used to efficiently compute centrality scores of a set of vertices.