MMN-4133

# An enumeration approach to network evolution

*Gábor Bacsó*;

*József Túri*;

## Abstract

A simple theoretical model of network evolution is discussed here.
In each step, we add a new vertex to the graph and it is allowed to connect it
to maximum degree vertices (hubs) only. Given a constant $p$, the probability of such a connection is $p$ for any hub. The initial (non-random) graph $G_1$ is arbitrary but here we investigate mostly the case when $G_1$ has one vertex.
We solve here some particular cases of the problem. using enumeration methods. We obtain not limit theorems but exact results for the parameters discussed.

Vol. 24 (2023), No. 2, pp. 625-634