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2022 A random graph of moderate density
Ágnes Backhausz, Tamás F. Móri
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Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/21-ECP444

Abstract

We analyse a randomly growing graph model in which the average degree is asymptotically equal to a constant times the square root of the number of vertices, and the clustering coefficient is rather small. In every step, we choose two vertices uniformly at random, check whether they are connected or not, and we either add a new edge or delete one and add a new vertex of degree two to the graph. This dependence on the status of the connection chosen vertices makes the total number of vertices random after n steps. We prove asymptotic normality for this quantity and also for the degree of a fixed vertex (with normalization n16). We also analyse the proportion of vertices with degree greater than a fixed multiple of the average degree, and the maximal degree.

Funding Statement

The research was partially supported by the NKFIH "Élvonal" KKP 133921 grant (to Á. B.), and by the Hungarian National Research, Development and Innovation Office NKFIH [grant number K 125569] (to T.F.M.).

Funding Statement

The research was partially supported by the NKFIH "Élvonal" KKP 133921 grant (to Á. B.), and by the Hungarian National Research, Development and Innovation Office NKFIH [grant number K 125569] (to T.F.M.).

Funding Statement

The research was partially supported by the NKFIH "Élvonal" KKP 133921 grant (to Á. B.), and by the Hungarian National Research, Development and Innovation Office NKFIH [grant number K 125569] (to T.F.M.).

Citation

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Ágnes Backhausz. Tamás F. Móri. "A random graph of moderate density." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/21-ECP444

Information

Received: 15 February 2021; Accepted: 26 December 2021; Published: 2022
First available in Project Euclid: 14 January 2022

Digital Object Identifier: 10.1214/21-ECP444

Subjects:
Primary: 05C80

Keywords: degree distribution , intermediate density , Random graphs

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