From one-way streets to percolation on random mixed graphs

In most studies, street networks are considered as undirected graphs while one-way streets and their effect on shortest paths usually ignored. Here, we first study the empirical of in about 140 cities world. Their presence induces a detour that persists over wide range distances is characterized by nonuniversal exponent. The one-ways pattern then twofold: they mitigate local traffic certain areas but create bottlenecks elsewhere. This leads naturally to considering mixed graph model 2d regular lattices with both links diluted variable fraction $p$ randomly directed which mimics network. We size strongly connected component (SCC) versus demonstrate existence threshold ${p}_{c}$ above SCC zero. show numerically this transition nontrivial for degree less than 4 provide some analytical argument. compute critical exponents confirm previous results showing define new universality class different from standard percolation. Finally, real-world can be understood random perturbations lattices. impact properties was already subject few mathematical our problem has also interesting connections percolation, classical statistical physics.