Simulation results on a triangle-based network evolution model

Fazekas, István; Barta, Attila; Noszály, Csaba

doi:10.33039/ami.2020.07.005

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2021

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“…Using this structure, the running time was reasonable. A more detailed explanation of the algorithm can be found in [20].…”

Section: Simulationsmentioning

confidence: 99%

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

Fazekas

Barta

2021

Mathematics

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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.

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“…Using this structure, the running time was reasonable. A more detailed explanation of the algorithm can be found in [20].…”

Section: Simulationsmentioning

confidence: 99%

“…We mention that our model was presented in our conference paper [18]. In that paper some preliminary theoretical results were announced together with some numerical evidence but without mathematical proofs.…”

Section: Introductionmentioning

confidence: 99%