A random graph model based on 3-interactions

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.

Key words and phrases. Martingales, random graphs, preferential attachment, scale free property.