# The $N$-stars network evolution model

## TL;DR

This paper introduces a novel network evolution model based on N-unit co-operations, resulting in power-law degree distributions, combining preferential attachment and uniform choice mechanisms.

## Contribution

It presents a new N-stars network evolution model that incorporates co-operations of N units and derives asymptotic power-law degree distributions.

## Key findings

- Power-law distributions for in-degrees and out-degrees.
- Model combines preferential attachment with uniform choice.
- Applicable to networks with N-unit co-operations.

## 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 co-operations 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.