Temporal percolation in activity driven networks

Abstract

We study the temporal percolation properties of temporal networks by taking as a representative example the recently proposed activity driven network model [N. Perra et al., Sci. Rep. 2, 469 (2012)]. Building upon an analytical framework based on a mapping to hidden variables networks, we provide expressions for the percolation time marking the onset of a giant connected component in the integrated network. In particular, we consider both the generating function formalism, valid for degree uncorrelated networks, and the general case of networks with degree correlations. We discuss the different limits of the two approach, indicating the parameter regions where the correlated threshold collapses onto the uncorrelated case. Our analytical prediction are confirmed by numerical simulations of the model. The temporal percolation concept can be fruitfully applied to study epidemic spreading on temporal networks. We show in particular how the susceptible-infected- removed model on an activity driven network can be mapped to the percolation problem up to a time given by the spreading rate of the epidemic process. This mapping allows to obtain addition information on this process, not available for previous approaches.

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• Statistical physics of vaccination
• Modern temporal network theory: A colloquium
• Percolation on complex networks: Theory and application
• The synchronized dynamics of time-varying networks
• Effect of risk perception on epidemic spreading in temporal networks
• Epidemic Spreading on Activity-Driven Networks with Attractiveness
• Epidemic Threshold in Continuous-Time Evolving Networks
• Contrasting Effects of Strong Ties on SIR and SIS Processes in Temporal Networks
• Percolation and Topological Properties of Temporal Higher-order Networks
• Epidemic Spreading and Aging in Temporal Networks with Memory
• Burstiness and tie reinforcement in time varying social networks
• Self-initiated behavioural change and disease resurgence on activity-driven networks
• Dynamic topologies of activity-driven temporal networks with memory
• Aging and percolation dynamics in a Non-Poissonian temporal network model
• Dynamic Hidden-Variable Network Models
• Temporal Dynamics of Connectivity and Epidemic Properties of Growing Networks
• Epidemic Thresholds of Infectious Diseases on Tie-Decay Networks
• Epidemics on evolving networks with varying degrees