Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge

Salnikov, Vsevolod; Cassese, Daniele; Lambiotte, Renaud; Jones, Nick

doi:10.48550/arxiv.1803.04410

Cited by 2 publications

(2 citation statements)

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“…Recently there has been growing interest in characterizing networked structures using geometrical and topological tools [1][2][3]. On one side an increasing number of works aim at unveiling the hidden geometry of networks using statistical mechanics [4][5][6][7][8][9][10][11], discrete geometry [12] and machine learning [13,14], on the other side topological data analysis is tailored to capture the structure of a large variety of network data [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Synchronization in network geometries with finite spectral dimension

Millán

Torres²,

Bianconi

2019

Phys. Rev. E

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Recently there is a surge of interest in network geometry and topology. Here we show that the spectral dimension plays a fundamental role in establishing a clear relation between the topological and geometrical properties of a network and its dynamics. Specifically we explore the role of the spectral dimension in determining the synchronization properties of the Kuramoto model. We show that the synchronized phase can only be thermodynamically stable for spectral dimensions above four and that phase entrainment of the oscillators can only be found for spectral dimensions greater than two. We numerically test our analytical predictions on the recently introduced model of network geometry called Complex Network Manifolds which displays a tunable spectral dimension.

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Section: Introductionmentioning

confidence: 99%

Synchronization in network geometries with finite spectral dimension

Millán

Torres²,

Bianconi

2019

Phys. Rev. E

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“…they have the hyperbolicity parameter δ=0, whereas the graphs with cycles can have a finite δ parameter. In recent years, Gromov hyperbolic graphs with a small parameter δ have been the subject of intensive research both for their mathematical properties [21][22][23][24][25] and applications [26][27][28][29][30][31][32][33][34]. A small hyperbolicity parameter is often associated with improved collective dynamics in natural and technological networks.…”

Section: Introductionmentioning

confidence: 99%

Self-organised criticality and emergent hyperbolic networks: blueprint for complexity in social dynamics

Tadić

2019

Eur. J. Phys.

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Online social dynamics based on human endeavours exhibit prominent complexity in the emergence of new features embodied in the appearance of collective social values. The vast amount of empirical data collected at various websites provides a unique opportunity to quantitative study od the underlying social dynamics in full analogy with complex systems in the physics laboratory. Here, we briefly describe the extent of these analogies and indicate the methods from other science disciplines that the physics theory can incorporate to provide the adequate description of human entities and principles of their self-organisation. We demonstrate the approach on two examples using the empirical data regarding the knowledge creation processes in online chats and questions-and-answers. Precisely, we describe the self-organised criticality as the acting mechanisms in the social knowledge-sharing dynamics and demonstrate the emergence of the hyperbolic geometry of the co-evolving networks that underlie these stochastic processes.

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Co-occurrence simplicial complexes in mathematics: identifying the holes of knowledge

Cited by 2 publications

References 0 publications

Synchronization in network geometries with finite spectral dimension

Synchronization in network geometries with finite spectral dimension

Self-organised criticality and emergent hyperbolic networks: blueprint for complexity in social dynamics

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