Complex networks in the framework of nonassociative geometry

Nesterov, Alexander I.; Villafuerte, Pablo Héctor Mata

doi:10.1103/physreve.101.032302

Cited by 4 publications

(4 citation statements)

References 41 publications

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“…Our approach is based on nonassociative geometry, a statistical description of complex networks, and the following assumptions [42,46,69]:…”

Section: Building Discrete Spacetimementioning

confidence: 99%

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Spacetime as a Complex Network and the Cosmological Constant Problem

Nesterov

2023

Universe

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We propose a promising model of discrete spacetime based on nonassociative geometry and complex networks. Our approach treats space as a simplicial 3-complex (or complex network), built from “atoms” of spacetime and entangled states forming n-dimensional simplices (n=1,2,3). At large scales, a highly connected network is a coarse, discrete representation of a smooth spacetime. We show that, for high temperatures, the network describes disconnected discrete space. At the Planck temperature, the system experiences phase transition, and for low temperatures, the space becomes a triangulated discrete space. We show that the cosmological constant depends on the Universe’s topology. The “foamy” structure, analogous to Wheeler’s “spacetime foam”, significantly contributes to the effective cosmological constant, which is determined by the Euler characteristic of the Universe.

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“…Our approach is based on nonassociative geometry, a statistical description of complex networks, and the following assumptions [42,46,69]:…”

Section: Building Discrete Spacetimementioning

confidence: 99%

“…Therefore, only fermionic graphs can be used for its description as a complex network. In what follows, we consider the modified version of the Hamiltonian proposed in [69],…”

Section: Spacetime As a Complex Networkmentioning

confidence: 99%

Spacetime as a Complex Network and the Cosmological Constant Problem

Nesterov

2023

Universe

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“…We are interested in the pure sparse network model with vanishing average node degree at zero temperature. We consider a particular model with the chemical potential defined by µ = T c ln(νN/ k ), where ν is a temperature-independent parameter [19][20][21]. As follows from our previous analysis, the chemical potential should be infinite at T = 0.…”

Section: A Phase Transitions In Sparse Networkmentioning

confidence: 99%

“…[18][19][20]. Further progress in this approach has been achieved by determining the network temperature in terms of empirical data, such as the number of nodes, average node degree, and exponent of the degree distribution [21].…”

Section: Introductionmentioning

confidence: 99%

Critical Phenomena in Complex Networks: from Scale-free to Random Networks

Nesterov,

Villafuerte

2020

Preprint

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Within the conventional statistical physics framework, we study critical phenomena in a class of network models with hidden variables controlling links between pairs of nodes. We find analytical expressions for the average node degree, the expected number of edges, and the Landau and Helmholtz free energies, as a function of the temperature and number of nodes. We show that the network's temperature is a parameter that controls the transition from unconnected graphs to power-degree (scale-free) and random graphs. With increasing temperature, the degree distribution is changed from power-degree, for lower temperatures, to a Poisson-like distribution for high temperatures. We also show that phase transition in the sparse networks leads to the fundamental structural changes in the network topology. Below the critical temperature, the graph is completely disconnected. Above the critical temperature, the graph becomes connected, and a giant component appears.

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Critical phenomena in complex networks: from scale-free to random networks

Nesterov,

Villafuerte

2023

Eur. Phys. J. B

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Complex networks in the framework of nonassociative geometry

Cited by 4 publications

References 41 publications

Spacetime as a Complex Network and the Cosmological Constant Problem

Spacetime as a Complex Network and the Cosmological Constant Problem

Critical Phenomena in Complex Networks: from Scale-free to Random Networks

Critical phenomena in complex networks: from scale-free to random networks

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