page_title: Multidimensional network
section_title: Diffusion processes on multilayer networks
hierarchical_section_title: Multidimensional network / Diffusion processes on multilayer networks
caption_attribution_description: English: Illustration of the random walk on the top of a special multilayer system, i.e. a multiplex network
context_page_description: In network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations. Increasingly sophisticated attempts to model real-world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international transport, ecology, psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, infrastructures and finance.
context_section_description: Diffusion processes are widely used in physics to explore physical systems, as well as in other disciplines as social sciences, neuroscience, urban and international transportation or finance. Recently, simple and more complex diffusive processes have been generalized to multilayer networks. One result common to many studies is that diffusion in multiplex networks, a special type of multilayer system, exhibits two regimes: 1) the weight of inter-layer links, connecting layers each other, is not high enough and the multiplex system behaves like two (or more) uncoupled networks; 2) the weight of inter-layer links is high enough that layers are coupled each other, raising unexpected physical phenomena. It has been shown that there is an abrupt transition between these two regimes.
  In fact, all network descriptors depending on some diffusive process, from centrality measures to community detection, are affected by the layer-layer coupling. For instance, in the case of community detection, low coupling (where information from each layer separately is more relevant than the overall structure) favors clusters within layers, whereas high coupling (where information from all layer simultaneously is more relevant than the each layer separately) favors cross-layer clusters.
  Diffusion reaction process on a multilayer system has been studied by Lazaridis et al. It is found that for the process  where A  and B are initially in different layers next they diffuse randomly and when they meet both disappear. It was found that in this model, due to the reaction, a kind of repulsion between A and B that delays their mixing and therefore their reaction.
caption: Illustration of a random walk on the top of a special multilayer system, i.e. a multiplex network
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