Diffusion geometry of multiplex and interdependent systems
arXiv:2006.13032 · doi:10.1103/PhysRevE.103.042301
Abstract
Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used in [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometry and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here, we firstly extend this class to families of distinct random walk dynamics -- including local and nonlocal information -- on multilayer networks -- a paradigm for biological, neural, social, transportation, biological and financial systems -- overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. Secondly, we characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.
References in corpus (43)
- Emergence of scaling in random networks
- Community structure in social and biological networks
- Maps of random walks on complex networks reveal community structure
- Multilayer Networks
- Networks beyond pairwise interactions: structure and dynamics
- Self-similarity of complex networks
- Hyperbolic Geometry of Complex Networks
- Diffusion dynamics on multiplex networks
- Mathematical Formulation of Multi-Layer Networks
- Quantum walks: a comprehensive review
- Structural measures for multiplex networks
- Lévy walks
- Random walks and diffusion on networks
- The physics of spreading processes in multilayer networks
- Layer aggregation and reducibility of multilayer interconnected networks
- Popularity versus Similarity in Growing Networks
- Origins of fractality in the growth of complex networks
- Random Walks on Multiplex Networks
- Navigability of Complex Networks
- Sustaining the Internet with Hyperbolic Mapping
- Centrality in Interconnected Multilayer Networks
- Explosive synchronization in adaptive and multilayer networks
- Random Walks, Markov Processes and the Multiscale Modular Organization of Complex Networks
- Laplacian Dynamics and Multiscale Modular Structure in Networks
- Self-similarity of complex networks and hidden metric spaces
- Social contagion models on hypergraphs
- Network Geometry
- Identifying modular flows on multilayer networks reveals highly overlapping organization in social systems
- Localization of maximal entropy random walk
- Spectral entropies as information-theoretic tools for complex network comparison
- Emergent Hyperbolic Network Geometry
- Topological data analysis of contagion maps for examining spreading processes on networks
- Hidden geometric correlations in real multiplex networks
- Quantum stochastic walks: A generalization of classical random walks and quantum walks
- Mapping higher-order network flows in memory and multilayer networks with Infomap
- Modular gateway-ness connectivity and structural core organization in maritime network science
- Efficient exploration of multiplex networks
- Navigable maps of structural brain networks across species
- Diffusion geometry unravels the emergence of functional clusters in collective phenomena
- Community Detection in Quantum Complex Networks
- Enhancing transport properties in interconnected systems without altering their structure
- Network depth: identifying median and contours in complex networks
- Towards a generalization of information theory for hierarchical partitions
Cited by in corpus (9)
- Network Geometry
- Multilayer Network Science: from Cells to Societies
- Network diffusion capacity unveiled by dynamical paths
- Convolutional Learning on Multigraphs
- Zoo Guide to Network Embedding
- Diffusion and synchronization dynamics reveal the multi-scale patterns of spatial segregation
- Non-equilibrium random walks on multiplex networks
- Gromov Centrality: A Multi-Scale Measure of Network Centrality Using Triangle Inequality Excess
- Latent geometry emerging from network-driven processes