Emergence of overlap in ensembles of spatial multiplexes and statistical mechanics of spatial interacting networks 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 datasets. We show that spatial multiplex 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 analyse the structure of interacting airport and railway networks in India, showing the effect of space in determining the link probability.

(12 pages, 4 figures) for downloading data see URL http://sites.google.com/site/satyammukherjee/pubs

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• Multilayer Networks
• The structure and dynamics of multilayer networks
• Measuring and modelling correlations in multiplex networks
• The synchronized dynamics of time-varying networks
• Synchronization in networks with multiple interaction layers
• Towards real-world complexity: an introduction to multiplex networks
• The new challenges of multiplex networks: measures and models
• Hidden geometric correlations in real multiplex networks
• k-Core percolation on multiplex networks
• Non-linear growth and condensation in multiplex networks
• Two distinct transitions in spatially embedded multiplex networks
• Link prediction based on path entropy
• Spreading of localized attacks in spatial multiplex networks
• Immunization strategy for epidemic spreading on multilayer networks
• Giant components in directed multiplex networks
• Growing Multiplex Networks with Arbitrary Number of Layers
• Correlations between weights and overlap in ensembles of weighted multiplex networks
• Optimal transport in multilayer networks for traffic flow optimization
• Optimization of synchronizability in multiplex networks
• k-core percolation on interdependent and interconnected multiplex networks
• Entropy of Spatial Network Ensembles
• Entropy-based link prediction in weighted networks
• Critical stretching of mean-field regimes in spatial networks
• Synchronized and mixed outbreaks of coupled recurrent epidemics
• Link persistence and conditional distances in multiplex networks
• Spatial networks with wireless applications
• The role of adjacency matrix degeneration in maximum entropy weighted network models
• Triadic percolation induces dynamical topological patterns in higher-order networks
• Interdependent transport via percolation backbones in spatial networks
• Approximation methods for the stability of complete synchronization on duplex networks
• Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes
• Observability transition in multiplex networks
• SimBins: An information-theoretic approach to link prediction in real multiplex networks
• Large algebraic connectivity fluctuations in spatial network ensembles imply a predictive advantage from node location information