Local topological moves determine global diffusion properties of hyperbolic higher-order networks
arXiv:2102.12885 · doi:10.1103/PhysRevE.104.054302
Abstract
From social interactions to the human brain, higher-order networks are key to describe the underlying network geometry and topology of many complex systems. While it is well known that network structure strongly affects its function, the role that network topology and geometry has on the emerging dynamical properties of higher-order networks is yet to be clarified. In this perspective, the spectral dimension plays a key role since it determines the effective dimension for diffusion processes on a network. Despite its relevance, a theoretical understanding of which mechanisms lead to a finite spectral dimension, and how this can be controlled, represents nowadays still a challenge and is the object of intense research. Here we introduce two non-equilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the interwined appearance of small-world behavior, -hyperbolicity and community structure. We show that different topological moves determining the non-equilibrium growth of the higher-order hyperbolic network models induce tunable values of the spectral dimension, showing a rich phenomenology which is not displayed in random graph ensembles. In particular, we observe that, if the topological moves used to construct the higher-order network increase the areavolume ratio, the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the areavolume ratio. Our work reveals a new link between the geometry of a network and its diffusion properties, contributing to a better understanding of the complex interplay between network structure and dynamics.
14 pages, 10 figures
References in corpus (19)
- Critical phenomena in complex networks
- A tool for filtering information in complex systems
- Abrupt Desynchronization and Extensive Multistability in Globally Coupled Oscillator Simplices
- Triadic closure as a basic generating mechanism of communities in complex networks
- Hyperbolic Graph Convolutional Neural Networks
- Random walks on hypergraphs
- Abrupt phase transition of epidemic spreading in simplicial complexes
- Fractal properties of quantum spacetime
- Higher-order simplicial synchronization of coupled topological signals
- Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks
- Simplicial SIS model in scale-free uniform hypergraph
- Emergent Complex Network Geometry
- Topological implications of negative curvature for biological and social networks
- The spectral dimension of generic trees
- Evolution of Cooperation in the Presence of Higher-Order Interactions: from Networks to Hypergraphs
- Network clique cover approximation to analyze complex contagions through group interactions
- D-dimensional oscillators in simplicial structures: odd and even dimensions display different synchronization scenarios
- Homological percolation transitions in growing simplicial complexes
- Cluster synchronization on hypergraphs