First passage percolation in sparse random graphs with boundary weights

TL;DR

This paper extends first passage percolation models on sparse random graphs by incorporating node boundary weights, providing approximate formulas for various propagation times over logarithmic time scales.

Contribution

It introduces a novel model with node boundary weights and derives approximate formulas for key propagation metrics in this extended setting.

Findings

Approximate formulas for typical first passage times

Results on flooding times and maximum flooding times

Analysis over logarithmic time scales

Abstract

A large and sparse random graph with independent exponentially distributed link weights can be used to model the propagation of messages or diseases in a network with an unknown connectivity structure. In this article we study an extended setting where also the nodes of the graph are equipped with nonnegative random weights which are used to model the effect of boundary delays across paths in the network. Our main results provide approximative formulas for typical first passage times, typical flooding times, and maximum flooding times in the extended setting, over a time scale logarithmic with respect to the network size.