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We propose a novel stochastic algorithm that randomly samples entire rows andcolumns of the matrix as a way to approximate an arbitrary matrix functionusing the power series expansion. This contrasts with existing Monte Carlomethods, which only work with one entry at a time, resulting in a significantlybetter convergence rate than the original approach. To assess the applicabilityof our method, we compute the subgraph centrality and total communicability ofseveral large networks. In all benchmarks analyzed so far, the performance ofour method was significantly superior to the competition, being able to scaleup to 64 CPU cores with remarkable efficiency.

A Fast Monte Carlo algorithm for evaluating matrix functions with application in complex networks