On the Topology of Higher-order Age-dependent Random Connection Models

In this paper, we investigate the potential of the age-dependent random connection model (ADRCM) with the aim of representing higher-order networks. A key contribution of our work are probabilistic limit results in large domains. More precisely, we first prove that the higher-order degree distributi...

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Bibliographic Details
Published in:Methodology and computing in applied probability Vol. 27; no. 2; p. 44
Main Authors: Hirsch, Christian, Juhasz, Peter
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2025
Springer Nature B.V
Subjects:
Age
Business and Management
Chemical elements
Clustering
Collaboration
Economics
Electrical Engineering
Exponents
Hypotheses
Life Sciences
Mathematics
Mathematics and Statistics
Networks
Power law
Statistics
Stochastic models
Theorems
Topology
Stochastic geometry
60D05
60G55
Random connection model
Higher-order network
60F05
Degree distribution
ISSN:1387-5841, 1573-7713
Online Access:Get full text
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Summary:In this paper, we investigate the potential of the age-dependent random connection model (ADRCM) with the aim of representing higher-order networks. A key contribution of our work are probabilistic limit results in large domains. More precisely, we first prove that the higher-order degree distributions have a power-law tail. Second, we establish central limit theorems for the edge counts and Betti numbers of the ADRCM in the regime where the degree distribution is light tailed. Moreover, in the heavy-tailed regime, we prove that asymptotically, the recentered and suitably rescaled edge counts converge to a stable distribution. We also propose a modification of the ADRCM in the form of a thinning procedure that enables independent adjustment of the power-law exponents for vertex and edge degrees. To apply the derived theorems to finite networks, we conduct a simulation study illustrating that the power-law degree distribution exponents approach their theoretical limits for large networks. It also indicates that in the heavy-tailed regime, the limit distribution of the recentered and suitably rescaled Betti numbers is stable. We demonstrate the practical application of the theoretical results to real-world datasets by analyzing scientific collaboration networks based on data from arXiv.
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-025-10173-7