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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| Published in: | Methodology and computing in applied probability Vol. 27; no. 2; p. 44 |
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| Language: | English |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 44 |
| Author | Hirsch, Christian Juhasz, Peter |
| Author_xml | – sequence: 1 givenname: Christian surname: Hirsch fullname: Hirsch, Christian email: hirsch@math.au.dk organization: Department of Mathematics, Aarhus University, DIGIT Center, Aarhus University – sequence: 2 givenname: Peter surname: Juhasz fullname: Juhasz, Peter organization: Department of Mathematics, Aarhus University |
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| Cites_doi | 10.1007/b97479 10.2307/270703 10.1214/22-EJP748 10.1016/j.physrep.2020.05.004 10.1016/j.spa.2019.04.014 10.1140/epjds/s13688-017-0114-8 10.25080/TCWV9851 10.1214/21-AAP1752 10.1214/14-AAP1006 10.1038/s41592-019-0686-2 10.1007/s11134-019-09625-y 10.1007/978-1-4612-0197-7_17 10.1155/2013/815035 10.1109/MCSE.2007.55 10.1017/apr.2021.13 10.1126/sciadv.1600028 10.1006/jmva.1993.1015 10.1214/17-AAP1371 10.1103/PhysRevE.106.034319 10.1126/science.286.5439.509 10.1371/journal.pone.0066506 10.1007/s10955-023-03122-6 10.1017/apr.2024.66 10.1103/PhysRevE.93.062311 10.1214/11-AOP697 10.1214/15-AOP1020 10.1214/11-AOP669 10.1214/16-AOP1098 10.1038/s41586-020-2649-2 10.1093/acprof:oso/9780198506263.001.0001 10.1017/apr.2020.42 10.1103/PhysRevE.93.032315 10.1214/aoap/1015345393 10.1137/070710111 |
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| SubjectTerms | 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 |
| Title | On the Topology of Higher-order Age-dependent Random Connection Models |
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