The birth of geometry in exponential random graphs

Akara-pipattana, Pawat; Chotibut, Thiparat; Evnin, Oleg

doi:10.1088/1751-8121/ac2474

Cited by 6 publications

(4 citation statements)

References 51 publications

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“…In conclusion, we hope that this work could provide a fertile ground for research at the interface between network theory and quantum gravity [67][68][69][70][71][72][73][74][75][76][77][78][79] and, more generally, quantum mechanics [29,[80][81][82][83][84][85][86][87], which has received increasing attention recently. Moreover, the hereby defined mass of simple and higher-order networks could prove itself as a relevant metric to characterize simple and higher-order networks coming from interdisciplinary applications.…”

Section: Discussionmentioning

confidence: 99%

The mass of simple and higher-order networks

Bianconi

2023

J. Phys. A: Math. Theor.

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We propose a theoretical framework that explains how the mass of simple and higher-order networks emerges from their topology and geometry. We use the discrete topological Dirac operator to define an action for a massless self-interacting topological Dirac field inspired by the Nambu–Jona-Lasinio model. The mass of the network is strictly speaking the mass of this topological Dirac field defined on the network; it results from the chiral symmetry breaking of the model and satisfies a self-consistent gap equation. Interestingly, it is shown that the mass of a network depends on its spectral properties, topology, and geometry. Due to the breaking of the matter–antimatter symmetry observed for the harmonic modes of the discrete topological Dirac operator, two possible definitions of the network mass can be given. For both possible definitions, the mass of the network comes from a gap equation with the difference among the two definitions encoded in the value of the bare mass. Indeed, the bare mass can be determined either by the Betti number β 0 or by the Betti number β 1 of the network. We provide numerical results on the mass of different networks, including random graphs, scale-free, and real weighted collaboration networks. We also discuss the generalization of these results to higher-order networks, defining the mass of simplicial complexes. The observed dependence of the mass of the considered topological Dirac field with the topology and geometry of the network could lead to interesting physics in the scenario in which the considered Dirac field is coupled with a dynamical evolution of the underlying network structure.

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Section: Discussionmentioning

confidence: 99%

The mass of simple and higher-order networks

Bianconi

2023

J. Phys. A: Math. Theor.

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“…It is this constraint that ultimately causes 2D combinatorial quantum gravity to be in a different universality class than Liouville quantum gravity [46]. Note also that some of these constraints on configuration space can alternatively be dynamically implemented by adding Kronecker delta terms to the Hamiltonian [48].…”

Section: Combinatorial Quantum Gravitymentioning

confidence: 99%

Combinatorial Quantum Gravity and Emergent 3D Quantum Behaviour

Trugenberger

2023

Universe

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We review combinatorial quantum gravity, an approach that combines Einstein’s idea of dynamical geometry with Wheeler’s “it from bit” hypothesis in a model of dynamical graphs governed by the coarse Ollivier–Ricci curvature. This drives a continuous phase transition from a random to a geometric phase due to a condensation of loops on the graph. In the 2D case, the geometric phase describes negative-curvature surfaces with two inversely related scales: an ultraviolet (UV) Planck length and an infrared (IR) radius of curvature. Below the Planck scale, the random bit character survives; chunks of random bits of the Planck size describe matter particles of excitation energy given by their excess curvature. Between the Planck length and the curvature radius, the surface is smooth, with spectral and Hausdorff dimension 2. At scales larger than the curvature radius, particles see the surface as an effective Lorentzian de Sitter surface, the spectral dimension becomes 3, and the effective slow dynamics of particles, as seen by co-moving observers, emerges as quantum mechanics in Euclidean 3D space. Since the 3D distances are inherited from the underlying 2D de Sitter surface, we obtain curved trajectories around massive particles also in 3D, representing the large-scale gravity interactions. We thus propose that this 2D model describes a generic holographic screen relevant for real quantum gravity.

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“…We note that however, due to space limitations, we cannot cover all the works at the interface between network science and quantum gravity, a field in which research interest is recently growing. This include work on causal sets [302,303], tensor field approaches [257,[304][305][306], combinatorial quantum gravity [307][308][309][310] and emergent random graph geometry [311][312][313][314] among other approaches [315].…”

Section: Introduction To Emergent Quantum Network Modelsmentioning

confidence: 99%

Complex quantum networks: a topical review

Nokkala,

Piilo,

Bianconi

2024

J. Phys. A: Math. Theor.

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These are exciting times for quantum physics as new quantum technologies are expected to soon transform computing at an unprecedented level. Simultaneously network science is ﬂourishing proving an ideal mathematical and computational framework to capture the complexity of large interacting systems. Here we provide a comprehensive and timely review of the rising ﬁeld of complex quantum networks. On one side, this subject is key to harness the potential of complex networks in order to provide design principles to boost and enhance quantum algorithms and quantum technologies. On the other side this subject can provide a new generation of quantum algorithms to infer signiﬁcant complex network properties. The ﬁeld features fundamental research questions as diverse as designing networks to shape Hamiltonians and their corresponding phase diagram, taming the complexity of many-body quantum systems with network theory, revealing how quantum physics and quantum algorithms can predict novel network properties and phase transitions, and studying the interplay between architecture, topology and performance in quantum communication networks. Our review covers all of these multifaceted aspects in a self-contained presentation aimed both at network-curious quantum physicists and at quantum-curious network theorists. We provide a framework that uniﬁes the ﬁeld of quantum complex networks along four main research lines: network-generalized, quantum-applied, quantum-generalized and quantum-enhanced. Finally we draw attention to the connections between these research lines, which can lead to new opportunities and new discoveries at the interface between quantum physics and network science.

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The birth of geometry in exponential random graphs

Cited by 6 publications

References 51 publications

The mass of simple and higher-order networks

The mass of simple and higher-order networks

Combinatorial Quantum Gravity and Emergent 3D Quantum Behaviour

Complex quantum networks: a topical review

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