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

István Fazekas and Attila Barta
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István Fazekas: Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary
Attila Barta: Faculty of Informatics, University of Debrecen, Kassai Street 26, 4028 Debrecen, Hungary

Mathematics, 2021, vol. 9, issue 23, 1-26

Abstract: 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 e α t , 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.

Keywords: network evolution; random graph; multi-type branching process; continuous-time branching process; 2- and 3-interactions; Malthusian parameter; Poisson process; life-length; extinction (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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