Diffusion geometry of multiplex and interdependent systems

Complex networks are characterized by latent geometries induced their topology or the dynamics on them. In latter case, different network-driven processes induce distinct geometric features that can be captured adequate metrics. Random walks, a proxy for broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used, Domenico [Phys. Rev. Lett. 118, 168301 (2017)] define class diffusion pinpoint functional mesoscale organization complex genuine perspective. Here we first extend this families random walk dynamics---including local nonlocal information---on multilayer networks---a paradigm biological, neural, social, transportation, financial systems---overcoming limitations such as presence isolated nodes disconnected components, typical real-world networks. We then characterize geometry synthetic empirical systems, highlighting role played search in shaping corresponding manifolds.