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Optimal subgraphs in geometric scale-free random graphs

Autor: Michielan, Riccardo, Stegehuis, Clara, Walter, Matthias

Geometric scale-free random graphs are popular models for networks that exhibit as heavy-tailed degree distributions, small-worldness and high clustering. In these models, vertices have weights that cause the heavy-tailed degrees and are embedded in

Externí odkaz: http://arxiv.org/abs/2404.14972

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Geometric random intersection graphs with general connection probabilities

Autor: Deijfen, Maria, Michielan, Riccardo

Publikováno v: J. Appl. Probab. 61 (2024) 1343-1360

Let $\mathcal{V}$ and $\mathcal{U}$ be the point sets of two independent homogeneous Poisson processes on $\mathbb{R}^d$. A graph $\mathcal{G}_\mathcal{V}$ with vertex set $\mathcal{V}$ is constructed by first connecting pairs of points $(v,u)$ with

Externí odkaz: http://arxiv.org/abs/2306.17507

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Localized geometry detection in scale-free random graphs

Autor: Bet, Gianmarco, Michielan, Riccardo, Stegehuis, Clara

We consider the problem of detecting whether a power-law inhomogeneous random graph contains a geometric community, and we frame this as an hypothesis testing problem. More precisely, we assume that we are given a sample from an unknown distribution

Externí odkaz: http://arxiv.org/abs/2303.02965

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Detecting hyperbolic geometry in networks: why triangles are not enough

Autor: Michielan, Riccardo, Litvak, Nelly, Stegehuis, Clara

Publikováno v: Phys. Rev. E 106, 2022

In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture many common

Externí odkaz: http://arxiv.org/abs/2206.01553

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Cliques in geometric inhomogeneous random graph

Autor: Michielan, Riccardo, Stegehuis, Clara

Publikováno v: Journal of Complex Networks, Volume 10, Issue 1, February 2022, cnac002

Many real-world networks were found to be highly clustered, and contain a large amount of small cliques. We here investigate the number of cliques of any size k contained in a geometric inhomogeneous random graph: a scale-free network model containin

Externí odkaz: http://arxiv.org/abs/2106.01875

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