title: Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting network ensembles.
abstract: Spatial networks range from the brain networks, to transportation networks and infrastructures. Recently interacting and multiplex networks are attracting great attention because their dynamics and robustness cannot be understood without treating at the same time several networks. Here we present maximal entropy ensembles of spatial multiplex and spatial interacting networks that can be used in order to model spatial multilayer network structures and to build null models of real data sets. We show that spatial multiplexes naturally develop a significant overlap of the links, a noticeable property of many multiplexes that can affect significantly the dynamics taking place on them. Additionally, we characterize ensembles of spatial interacting networks and we analyze the structure of interacting airport and railway networks in India, showing the effect of space in determining the link probability.
authors.affiliation: Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA.
authors.forename: Arda
authors.initials: A
authors.lastname: Halu
authors.affiliation: Kellogg School of Management, Northwestern University, Evanston, Illinois 60208, USA.
authors.forename: Satyam
authors.initials: S
authors.lastname: Mukherjee
authors.affiliation: School of Mathematical Sciences, Queen Mary University of London, London E1 4NS, United Kingdom.
authors.forename: Ginestra
authors.initials: G
authors.lastname: Bianconi