Interdependent transport via percolation backbones in spatial networks

Percolation on spatial anisotropic networks*

“…For example, there are far more highways connecting two neighboring cities than highways that stretch directly between two remote cities. Thus, to model this kind of networks recent studies have introduced spatial constraints to the distribution of edge lengths [35][36][37][38][39][40][41][42][43][44] helping us better understand realistic networks in which the link lengths are spatially limited. In our model the spatial constraints are enforced by using an exponential distribution for the edge lengths (see equation ( 1)) as suggested by Danziger et al [35] based on realistic networks and similar to earlier studies made by Waxman [41] and Bradde et al [42].…”

Percolation on spatial anisotropic networks

“…Various network structures have been proposed and studied as models for different systems -From the Erdos-Renyi's model which was introduced back in 1959 [23][24][25][26], through scale-free networks [27], multilayer networks [28], multiplex networks [29], interdependent networks [30][31][32][33] and networks of networks [33,34] -All of them proposing a variety and a growing complexity of the connections between the particular nodes, in one or more networks. Recent studies have introduced spatial constraints to the distribution of edge lengths [35][36][37][38][39][40][41][42][43][44] helping us better understand realistic networks in which the link lengths are spatially limited. The spatial constraints are enforced in the model by using an exponential distribution for the edge lengths as suggested by Danziger et al [35] based on realistic networks and similar to earlier studies made by Waxman [41] and Bradde et al [42].…”