Local topological moves determine global diffusion properties of hyperbolic higher-order networks
Year: 2021
Authors: Millàn A.P., Ghorbanchian R., Defenu N., Battiston F., Bianconi G.
Autors Affiliation: Vrije Univ Amsterdam, Amsterdam UMC, Dept Clin Neurophysiol, De Boelelaan 1117, Amsterdam, Netherlands; MEG Ctr, Amsterdam Neurosci, De Boelelaan 1117, Amsterdam, Netherlands; Queen Mary Univ London, Sch Math Sci, Mile End Rd, London E1 4NS, England; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland; Cent European Univ, Dept Network & Data Sci, A-1100 Vienna, Austria; Alan Turing Inst, British Lib, 96 Euston Rd, London NW1 2DB, England.
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 higherorder 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, still represents a challenge and is the object of intense research. Here, we introduce two nonequilibrium models of hyperbolic higher-order networks and we characterize their network topology and geometry by investigating the intertwined appearance of small-world behavior, delta-hyperbolicity, and community structure. We show that different topological moves, determining the nonequilibrium growth of the higher-order hyperbolic network models, induce tuneable 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 area/volume ratio, then the spectral dimension continuously decreases, while the opposite effect is observed if the topological moves decrease the area/volume 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.
Journal/Review: PHYSICAL REVIEW E
Volume: 104 (5) Pages from: 54302-1 to: 54302-14
More Information: A.P.M. is supported by ZonMw and the Dutch Epilepsy Foundation, Project No. 95105006. F.B. acknowledges partial supp ort from the ERC Synergy Grant No. 810115 (DYNASNET). This work is also supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster) and by the Royal Society (Grant No. IECNSFC191147 to G.B.).KeyWords: Spectral Dimension; Complex; ModelsDOI: 10.1103/PhysRevE.104.054302Citations: 13data from “WEB OF SCIENCE” (of Thomson Reuters) are update at: 2024-11-17References taken from IsiWeb of Knowledge: (subscribers only)