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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 thespreading agent has a limited lifetime at nodes: disease spreading (recoverytime), diffusion of rumors (lifetime of information), and passenger routing(maximum acceptable time between transfers). Here, we introduce weighted eventgraphs as a powerful and fast framework for studying connectivity determined bytime-respecting paths where the allowed waiting times between contacts have anupper limit. We study percolation on the weighted event graphs and in theunderlying temporal networks, with simulated and real-world networks. We showthat this type of temporal-network percolation is analogous to directedpercolation, and that it can be characterized by multiple order parameters.

Mapping temporal-network percolation to weighted, static event graphs