We propose a novel stochastic algorithm that randomly samples entire rows and
columns of the matrix as a way to approximate an arbitrary matrix function.
This contrasts with the "classical" Monte Carlo method which only works with
one entry at a time, resulting in a significant better convergence rate than
the "classical" approach. To assess the applicability of our method, we compute
the subgraph centrality and total communicability of several large networks. In
all benchmarks analyzed so far, the performance of our method was significantly
superior to the competition, being able to scale up to 64 CPU cores with a
remarkable efficiency.Comment: Submitted to the Journal of Scientific Computin