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

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 alpha t, where alpha 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.

Automated summary

A continuous-time network evolution model based on 2- and 3-interactions is considered, with the evolution of the edges and triangles governed by a multi-type continuous-time branching process. The study focuses on the limiting behavior of the network, proving that the number of triangles and edges have the same magnitude on the event of non-extinction. The probability of extinction and degree process of a fixed vertex are also studied, with results illustrated by simulations.