Sublinear Algorithms for Local Graph Centrality Estimation

We study the complexity of local graph centrality estimation, with the goal of approximating the centrality score of a given target node while exploring only a sublinear number of nodes/arcs of the graph and performing a sublinear number of elementary operations. We develop a technique, that we apply to the PageRank and Heat Kernel centralities, for building a low-variance score estimator through a local exploration of the graph. We obtain an algorithm that, given any node in any graph of m arcs, with probability (1 - delta) computes a multiplicative (1 +/- epsilon)-approximation of its score by examining only (O) over tilde (min(m(2/3)Delta(1/3)d(-2/3), m(4/5) d(-3/5))) nodes/arcs, where Delta and d are respectively the maximum and average outdegree of the graph (omitting for readability poly(epsilon(-1)) and polylog(delta(-1)) factors). A similar bound holds for computational cost. We also prove a lower bound of Omega(min(m(1/2)Delta(1/2)d(-1/2), m(2/3)d(-1/3))) for both query complexity and computational complexity. Moreover, our technique yields a (O) over tilde (n(2/3))-queries algorithm for an n-node graph in the access model of Brautbar et al. [1], widely used in social network mining; we show this algorithm is optimal up to a sublogarithmic factor. These are the first algorithms yielding worst-case sublinear bounds for general directed graphs and any choice of the target node.