Interdisciplinary and physics challenges of Network Theory

Abstract

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and dynamics. After almost twenty years of the field, new challenges lie ahead. These challenges concern the multilayer structure of most of the networks, the formulation of a network geometry and topology, and the development of a quantum theory of networks. Making progress on these aspects of network theory can open new venues to address interdisciplinary and physics challenges including progress on brain dynamics, new insights into quantum technologies, and quantum gravity.

(7 pages, 4 figures)

References in corpus (22)

• The Quantum Internet
• The structure and dynamics of multilayer networks
• Critical phenomena in complex networks
• Hyperbolic Geometry of Complex Networks
• Diffusion dynamics on multiplex networks
• Multirelational Organization of Large-scale Social Networks in an Online World
• Network Physiology reveals relations between network topology and physiological function
• Emergence of network features from multiplexity
• Navigability of Complex Networks
• Sustaining the Internet with Hyperbolic Mapping
• Avoiding catastrophic failure in correlated networks of networks
• Quantum Graphity: a model of emergent locality
• Network Controllability Is Determined by the Density of Low In-Degree and Out-Degree Nodes
• Generalized Bose-Fermi statistics and structural correlations in weighted networks
• Network Cosmology
• Emergent Complex Network Geometry
• Quantum transport on small-world networks: A continuous-time quantum walk approach
• Topological implications of negative curvature for biological and social networks
• Complex Quantum Network Geometries: Evolution and Phase Transitions
• Geometry, pregeometry and beyond
• Phase transition of light on complex quantum networks
• A geometric entropy detecting the Erdös-Rényi phase transition

Cited by in corpus (69)

• Networks beyond pairwise interactions: structure and dynamics
• The Kuramoto model in complex networks
• Explosive higher-order Kuramoto dynamics on simplicial complexes
• Network Geometry
• Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
• Multilayer Networks in a Nutshell
• Network Analysis of Particles and Grains
• Machine learning meets network science: dimensionality reduction for fast and efficient embedding of networks in the hyperbolic space
• Synchronization in networks with multiple interaction layers
• Emergent Hyperbolic Network Geometry
• Network geometry with flavor: from complexity to quantum geometry
• Complex Networks from Classical to Quantum
• Complex systems: physics beyond physics
• Higher-order percolation processes on multiplex hypergraphs
• Centralities of Nodes and Influences of Layers in Large Multiplex Networks
• Weighted Growing Simplicial Complexes
• Beyond the clustering coefficient: A topological analysis of node neighbourhoods in complex networks
• Functional Multiplex PageRank
• Clustering implies geometry in networks
• Simplicial complexes: higher-order spectral dimension and dynamics
• Synchronization in Network Geometries with Finite Spectral Dimension
• Extracting Information from Multiplex Networks
• Reconfigurable optical implementation of quantum complex networks
• Topological Percolation on Hyperbolic Simplicial Complexes
• The spectral dimension of simplicial complexes: a renormalization group theory
• Network Geometry and Complexity
• Complex Quantum Networks: a Topical Review
• Dense Power-law Networks and Simplicial Complexes
• Percolation on branching simplicial and cell complexes and its relation to interdependent percolation
• The inherent community structure of hyperbolic networks
• Embedding Graphs in Lorentzian Spacetime
• Complex Quantum Networks: From Universal Breakdown to Optimal Transport
• The higher-order spectrum of simplicial complexes: a renormalization group approach
• Persistent homology of unweighted complex networks via discrete Morse theory
• Emergence of the Circle in a Statistical Model of Random Cubic Graphs
• Right-side-stretched multifractal spectra indicate small-worldness in networks
• Continuous-time quantum walk spatial search on the Bollobás scale-free network
• Self-Organised Criticality and Emergent Hyperbolic Networks -- Blueprint for Complexity in Social Dynamics
• Renormalization group for link percolation on planar hyperbolic manifolds
• Bipartite separability and non-local quantum operations on graphs
• Geometry, Topology and Simplicial Synchronization
• Model-independent methods for embedding directed networks into Euclidean and hyperbolic spaces
• An Unsupervised Framework for Comparing Graph Embeddings
• Emergent Space-Time via a Geometric Renormalization Method
• Edge states in a two-dimensional quantum walk with disorder
• Renormalization group theory of percolation on pseudo-fractal simplicial and cell complexes
• Functional control of network dynamics using designed Laplacian spectra
• Optimisation of the coalescent hyperbolic embedding of complex networks
• Radial and circular synchronization clusters in extended starlike network of van der Pol oscillators
• Continuous variables graph states shaped as complex networks: optimization and manipulation
• Dynamics of "comb-of-comb" networks
• Convergence of Combinatorial Gravity
• Quantum statistics in Network Geometry with Fractional Flavor
• Interacting quantum walk on a graph
• Local probe for connectivity and coupling strength in quantum complex networks
• Layered Complex Networks as Fluctuation Amplifiers
• Forman-Ricci curvature and Persistent homology of unweighted complex networks
• Real-Space Visualization of Quantum Phase Transition by Network Topology
• Coherent trapping in small quantum networks
• Navigability of Random Geometric Graphs in the Universe and Other Spacetimes
• Spontaneous repulsion in the $A+B\to 0$ reaction on coupled networks
• Complex Networks in the Framework of Nonassociative Geometry
• Local topological moves determine global diffusion properties of hyperbolic higher-order networks
• Non-Markovianity over ensemble averages in quantum complex networks
• Network structure and dynamics of effective models of non-equilibrium quantum transport
• Network architecture of energy landscapes in mesoscopic quantum systems
• Topological data analysis of truncated contagion maps
• Efficient excitation-transfer across fully connected networks via local-energy optimization
• Unveiling hidden features of the Kitaev model through a complex-network analysis