Directed percolation in temporal networks

Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation information or accessibility public transport system over time, have been among main contemporary areas study in complex systems for last decade. However, while isotropic percolation theory successfully describes connectivity static similar description has not yet developed networks. Here address this problem formalize mapping concept network to theory. We show that limited-waiting-time reachability, generic notion constrained displays directed phase transition connectivity. Consequently, critical properties processes networks be estimated by set known exponents characterising universality class. This result is robust across diverse models with different topological heterogeneities, using our methodology we uncover transitions real too. These findings open up an avenue apply theory, concepts from well-developed literature