Mapping temporal-network percolation to weighted, static event graphs

TL;DR

This paper introduces weighted event graphs to analyze percolation in temporal networks, accounting for contact timing correlations and limited contact durations, with applications to real-world spreading processes.

Contribution

It presents a novel framework linking temporal-network percolation to weighted, static event graphs, enabling efficient analysis of time-respecting paths with upper waiting time limits.

Findings

Percolation in temporal networks can be modeled using weighted event graphs.

The approach is analogous to directed percolation and involves multiple order parameters.

The method is validated on simulated and real-world networks.

Abstract

Many processes of spreading and diffusion take place on temporal networks, and their outcomes are influenced by correlations in the times of contact. These correlations have a particularly strong influence on processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). Here, we introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters.