The $N$-stars network evolution model

Abstract

A new network evolution model is introduced in this paper. The model is based on co-operations of N units. The units are the nodes of the network and the cooperations are indicated by directed links. At each evolution step N units co-operate which formally means that they form a directed N -star subgraph. At each step either a new unit joins to the network and it co-operates with N − 1 old units or N old units co-operate. During the evolution both preferential attachment and uniform choice are applied. Asymptotic power law distributions are obtained both for the in-degrees and the out-degrees.