# Barab\'asi-Albert random graph with multiple type edges with perturbation

## TL;DR

This paper introduces a perturbed version of the Barabási-Albert model with multiple edge types, demonstrating that perturbation leads to a deterministic asymptotic degree distribution, unlike the non-perturbed case.

## Contribution

It extends the Barabási-Albert model by incorporating perturbations and proves the existence of a deterministic asymptotic degree distribution in this setting.

## Key findings

- Perturbation makes the degree distribution deterministic.
- Asymptotic degree distribution depends on edge type proportions.
- Existence of generalized asymptotic degree distribution is established.

## Abstract

In this paper we introduce the perturbed version of the Barab\'asi-Albert random graph with multiple type edges and prove the existence of the (generalized) asymptotic degree distribution. Similarly to the non-perturbed case, the asymptotic degree distribution depends on the almost sure limit of the proportion of edges of different types. However, if there is perturbation then the resulting degree distribution will be deterministic, which is a major difference compared to the non-perturbed case.