In their 2022 paper "Effective resistance against pandemics: Mobility network sparsification for high-fidelity epidemic simulations", Mercier et al. sparsify according to the effective resistances of edges in order to reduce the computational cost of simulating epidemics. Empirically, they observe that the resulting sparse network retains many aspects of an SIR (susceptible, infected, recovered) model, even when fewer than 10% of edges are kept.

We generated a sequence of synthetic networks, and for each checked if effective-resistance sparsification preserved infection dynamics. We observed a strong link between the degree distribution of the original graph and the answer to this question. Interestingly, the answer seems to be no for short-tailed degree distributions, yes for a specific regime of heavy-tailed ones, and again no when the tail of the degree distribution becomes too heavy.

The goal of the project is to investigate this trichotomy, formulate a conjecture for some aspect of the observed behavior, and establish a sketch of proof.

How to Apply: send your CV and transcript to Raphaël at raphael.fua@epfl.ch .