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Spatial networks range from the brain networks, to transportation networksand infrastructures. Recently interacting and multiplex networks are attractinggreat attention because their dynamics and robustness cannot be understoodwithout treating at the same time several networks. Here we present maximalentropy ensembles of spatial multiplex and spatial interacting networks thatcan be used in order to model spatial multilayer network structures and tobuild null models of real datasets. We show that spatial multiplex naturallydevelop a significant overlap of the links, a noticeable property of manymultiplexes that can affect significantly the dynamics taking place on them.Additionally, we characterize ensembles of spatial interacting networks and weanalyse the structure of interacting airport and railway networks in India,showing the effect of space in determining the link probability.

Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks ensembles