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

TL;DR

This paper introduces a fast Monte Carlo algorithm that efficiently approximates matrix functions by sampling entire rows and columns, significantly improving convergence and scalability for large network analysis tasks.

Contribution

The paper presents a novel stochastic sampling method for matrix functions that outperforms existing entry-wise Monte Carlo approaches in speed and scalability.

Findings

Superior performance in computing subgraph centrality and communicability

Scales efficiently up to 64 CPU cores

Outperforms existing Monte Carlo methods in benchmarks

Abstract

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 using the power series expansion. This contrasts with existing Monte Carlo methods, which only work with one entry at a time, resulting in a significantly better convergence rate than the original 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 remarkable efficiency.