Abstract
The dynamics of diffusion-like processes on temporal networks are influenced by correlations in the times of contacts. This influence is particularly strong for 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). 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.
Highlights
Contact network structure plays an important role in many dynamical processes, in particular in diffusion-like phenomena[1,2]
The weighted event graph representation of G is defined as the graph D = (E, ED, w) where the set of nodes E is the set of events in G and the edges eD ∈ ED represent the adjacency of the events eD = e → e′ with weights defined as temporal distances w(eD) = t′ − t
We have introduced a new representation of temporal networks by mapping them into event graphs that are static, weighted, directed, and acyclic
Summary
Contact network structure plays an important role in many dynamical processes, in particular in diffusion-like phenomena[1,2]. The temporal properties of networks have been shown to strongly influence spreading dynamics[3,4,5] This is (a) because spreading processes must follow causal, time-respecting paths spanned by sequences of contacts[6,7,8,9,10] and (b) because the speed and ability of spreading processes to percolate through the contact structure are affected by temporal inhomogeneities such as the burstiness of contacts, visible as broad inter-contact time distributions[11,12,13,14,15] and correlated contact times[16,17,18]. The subset of paths corresponding to a specific value of δt can be quickly extracted from the weighted event graph by thresholding it
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