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.
arXiv comment14 pages, 10 figures
References in corpus (60)
- Critical phenomena in complex networks
- Networks beyond pairwise interactions: structure and dynamics
- Why social networks are different from other types of networks
- A tool for filtering information in complex systems
- Simplicial models of social contagion
- A roadmap for the computation of persistent homology
- Random walks and diffusion on networks
- Evolutionary dynamics of higher-order interactions in social networks
- Spectral Dimension of the Universe
- Explosive higher-order Kuramoto dynamics on simplicial complexes
- Continuous-Time Quantum Walks: Models for Coherent Transport on Complex Networks
- 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
- Social contagion models on hypergraphs
- Topological Signal Processing over Simplicial Complexes
- Random walks on hypergraphs
- A Model for Social Networks
- Multiorder Laplacian for synchronization in higher-order networks
- The effect of heterogeneity on hypergraph contagion models
- Abrupt phase transition of epidemic spreading in simplicial complexes
- Simplicial Activity Driven Model
- Fractal properties of quantum spacetime
- Emergent Hyperbolic Network Geometry
- Simplicial complexes and complex systems
- Topological data analysis of contagion maps for examining spreading processes on networks
- The Large Scale Curvature of Networks
- Network geometry with flavor: from complexity to quantum geometry
- The Influence of Network Topology on Sound Propagation in Granular Materials
- Coupled Dynamics on Hypergraphs: Master Stability of Steady States and Synchronization
- Higher-order simplicial synchronization of coupled topological signals
- Criticality and Phase Diagram of Quantum Long-Range models
- Interdisciplinary and physics challenges of Network Theory
- Universal nonlinear infection kernel from heterogeneous exposure on higher-order networks
- Simplicial SIS model in scale-free uniform hypergraph
- Emergent Complex Network Geometry
- Fixed Points Structure & Effective Fractional Dimension for O(N) Models with Long-Range Interactions
- Probing the quantum nature of spacetime by diffusion
- Beyond the clustering coefficient: A topological analysis of node neighbourhoods in complex networks
- Simplicial complexes: higher-order spectral dimension and dynamics
- Synchronization in Network Geometries with Finite Spectral Dimension
- The spectral dimension of the branched polymers phase of two-dimensional quantum gravity
- Clustering Drives Assortativity and Community Structure in Ensembles of Networks
- Topological implications of negative curvature for biological and social networks
- The spectral dimension of generic trees
- Spectral dimensions of hierarchical scale-free networks with shortcuts
- 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
- Network Geometry and Complexity
- Critical fluctuations in spatial complex networks
- Homological Percolation and the Euler Characteristic
- One-dimensional long-range percolation: a numerical study
- The inverse Mermin-Wagner theorem for classical spin models on graphs
- Homological percolation transitions in growing simplicial complexes
- Complex networks with tuneable dimensions as a universality playground
- Spectral properties of hyperbolic nano-networks with tunable aggregation of simplexes
- Renormalization group for link percolation on planar hyperbolic manifolds
- Spectral renormalization group theory on networks
- Cluster synchronization on hypergraphs