A random graph model based on 3-interactions

TL;DR

This paper introduces a discrete-time random graph model driven by 3-interactions, demonstrating its scale-free nature and analyzing the asymptotic behavior of vertex weights.

Contribution

It presents a novel 3-interaction based model and proves its scale-free property along with the asymptotics of vertex weights.

Findings

The model exhibits scale-free degree distribution.

Vertices with higher weights are more likely to participate in future interactions.

Asymptotic behavior of fixed vertex weights is characterized.

Abstract

We consider a random graph model evolving in discrete time-steps that is based on 3-interactions among vertices. Triangles, edges and vertices have different weights; objects with larger weight are more likely to participate in future interactions. We prove the scale free property of the model by exploring the asymptotic behaviour of the weight distribution. We also find the asympotics of the weight of a fixed vertex.