A Continuous-Time Network Evolution Model Describing 2- and 3-Interactions

Autor:	István Fazekas, Attila Barta
Jazyk:	angličtina
Rok vydání:	2021
Předmět:	network evolution random graph multi-type branching process continuous-time branching process 2- and 3-interactions Malthusian parameter Mathematics QA1-939
Zdroj:	Mathematics, Vol 9, Iss 23, p 3143 (2021)
Druh dokumentu:	article
ISSN:	2227-7390 52707490
DOI:	10.3390/math9233143
Popis:	A continuous-time network evolution model is considered. The evolution of the network is based on 2- and 3-interactions. 2-interactions are described by edges, and 3-interactions are described by triangles. The evolution of the edges and triangles is governed by a multi-type continuous-time branching process. The limiting behaviour of the network is studied by mathematical methods. We prove that the number of triangles and edges have the same magnitude on the event of non-extinction, and it is eαt, where α is the Malthusian parameter. The probability of the extinction and the degree process of a fixed vertex are also studied. The results are illustrated by simulations.
Databáze:	Directory of Open Access Journals
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