Directed extended-range percolation (opens in new tab)

While for standard percolation directionality is known to increase the combinatorial complexity of percolation, here we show that when connectivity is ensured by paths of length $R\geq 2$, network directionality, impeding backtracking, can significantly reduce the complexity of percolation. To illustrate this finding, we introduce Directed Extended-Range Percolation (DERP), defined directed networks with non-reciprocal edges, motivated by appl...