Silvia Bartolucci, Fabio Caccioli, Francesco Caravelli, Pierpaolo Vivo
SciPost Phys. 11, 088 (2021) ·
published 4 November 2021
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We derive an approximate but explicit formula for the Mean First Passage Time
of a random walker between a source and a target node of a directed and
weighted network. The formula does not require any matrix inversion, and it
takes as only input the transition probabilities into the target node. It is
derived from the calculation of the average resolvent of a deformed ensemble of
random sub-stochastic matrices $H=\langle H\rangle +\delta H$, with $\langle
H\rangle$ rank-$1$ and non-negative. The accuracy of the formula depends on the
spectral gap of the reduced transition matrix, and it is tested numerically on
several instances of (weighted) networks away from the high sparsity regime,
with an excellent agreement.
